14 Trajectory Analysis

In this lab, we will analyze a single cell RNA-seq dataset that will teach us about several methods to infer the differentiation trajectory of a set of cells. These methods can order a set of individual cells along a path / trajectory / lineage, and assign a pseudotime value to each cell that represents where the cell is along that path. This can be a starting point for further analysis to determine gene expression programs driving interesting cell phenotypes. As you are running the code, think about how the algorithms work and what you like and do not like about the assumptions and utilities provided by the algorithm.

14.1 Load settings and packages

library(SingleCellExperiment)  # way to store single cell data

## Loading required package: SummarizedExperiment

## Loading required package: GenomicRanges

## Loading required package: stats4

## Loading required package: BiocGenerics

## Loading required package: parallel

## 
## Attaching package: 'BiocGenerics'

## The following objects are masked from 'package:parallel':
## 
##     clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
##     clusterExport, clusterMap, parApply, parCapply, parLapply,
##     parLapplyLB, parRapply, parSapply, parSapplyLB

## The following object is masked from 'package:liger':
## 
##     normalize

## The following objects are masked from 'package:dplyr':
## 
##     combine, intersect, setdiff, union

## The following object is masked from 'package:Matrix':
## 
##     which

## The following objects are masked from 'package:stats':
## 
##     IQR, mad, sd, var, xtabs

## The following objects are masked from 'package:base':
## 
##     anyDuplicated, append, as.data.frame, basename, cbind, colnames,
##     dirname, do.call, duplicated, eval, evalq, Filter, Find, get, grep,
##     grepl, intersect, is.unsorted, lapply, Map, mapply, match, mget,
##     order, paste, pmax, pmax.int, pmin, pmin.int, Position, rank,
##     rbind, Reduce, rownames, sapply, setdiff, sort, table, tapply,
##     union, unique, unsplit, which, which.max, which.min

## Loading required package: S4Vectors

## 
## Attaching package: 'S4Vectors'

## The following object is masked from 'package:plyr':
## 
##     rename

## The following objects are masked from 'package:dplyr':
## 
##     first, rename

## The following object is masked from 'package:Matrix':
## 
##     expand

## The following object is masked from 'package:base':
## 
##     expand.grid

## Loading required package: IRanges

## 
## Attaching package: 'IRanges'

## The following object is masked from 'package:plyr':
## 
##     desc

## The following object is masked from 'package:sp':
## 
##     %over%

## The following objects are masked from 'package:dplyr':
## 
##     collapse, desc, slice

## Loading required package: GenomeInfoDb

## Loading required package: Biobase

## Welcome to Bioconductor
## 
##     Vignettes contain introductory material; view with
##     'browseVignettes()'. To cite Bioconductor, see
##     'citation("Biobase")', and for packages 'citation("pkgname")'.

## Loading required package: DelayedArray

## Loading required package: matrixStats

## 
## Attaching package: 'matrixStats'

## The following objects are masked from 'package:Biobase':
## 
##     anyMissing, rowMedians

## The following object is masked from 'package:plyr':
## 
##     count

## The following object is masked from 'package:dplyr':
## 
##     count

## Loading required package: BiocParallel

## 
## Attaching package: 'DelayedArray'

## The following objects are masked from 'package:matrixStats':
## 
##     colMaxs, colMins, colRanges, rowMaxs, rowMins, rowRanges

## The following objects are masked from 'package:base':
## 
##     aperm, apply, rowsum

## 
## Attaching package: 'SummarizedExperiment'

## The following object is masked from 'package:Seurat':
## 
##     Assays

library(destiny)  # diffusion maps and diffusion pseudotime

## 
## Attaching package: 'destiny'

## The following object is masked from 'package:SummarizedExperiment':
## 
##     distance

## The following object is masked from 'package:GenomicRanges':
## 
##     distance

## The following object is masked from 'package:IRanges':
## 
##     distance

library(scater)  # related SingleCellExperiment package

## 
## Attaching package: 'scater'

## The following objects are masked from 'package:liger':
## 
##     runTSNE, runUMAP

library(clusterExperiment)

## Registered S3 methods overwritten by 'registry':
##   method               from 
##   print.registry_field proxy
##   print.registry_entry proxy

## 
## Attaching package: 'clusterExperiment'

## The following object is masked from 'package:scater':
## 
##     plotHeatmap

library(gam)

## Loading required package: splines

## Loading required package: foreach

## Loaded gam 1.16.1

library(corrplot)

## corrplot 0.84 loaded

## 
## Attaching package: 'corrplot'

## The following object is masked from 'package:destiny':
## 
##     colorlegend

library(ggplot2)
library(ggthemes)

## 
## Attaching package: 'ggthemes'

## The following object is masked from 'package:cowplot':
## 
##     theme_map

library(ggbeeswarm)
library(dplyr)
library(cowplot)
library(RColorBrewer)
library(knitr)

# Set folder location for saving output files. This is also the same location as input data.
mydir <- "data/trajectory/"
setwd("/home/rstudio/materials/") 

# Objects to save.
Rda.destiny.path <- paste0(mydir, "trajectory_destiny.Rda")
Rda.slingshot.path <- paste0(mydir, "trajectory_slingshot.Rda")

set.seed(1)  # set a seed for your random number generator to get reproducible results 
opts_chunk$set(fig.align = "center")

14.2 First look at the differentiation data from Deng et al.

We will use a nice SMART-Seq2 single cell RNA-seq data from Single-Cell RNA-Seq Reveals Dynamic, Random Monoallelic Gene Expression in Mammalian Cells. Here is one relevant detail from their paper: “To investigate allele-specific gene expression at single-cell resolution, we isolated 269 individual cells dissociated from in vivo F1 embryos (CAST/EiJ × C57BL/6J, hereafter abbreviated as CAST and C57, respectively) from oocyte to blastocyst stages of mouse preimplantation development (PD)”

# Read in single cell data.
path.deng <- paste0(mydir, "deng-reads.rds")
deng_SCE <- readRDS(path.deng)

# What class is the deng_SCE object, and how is it organized?
class(deng_SCE)

## [1] "SingleCellExperiment"
## attr(,"package")
## [1] "SingleCellExperiment"

structure(deng_SCE)

## class: SingleCellExperiment 
## dim: 22431 268 
## metadata(0):
## assays(2): counts logcounts
## rownames(22431): Hvcn1 Gbp7 ... Sox5 Alg11
## rowData names(10): feature_symbol is_feature_control ... total_counts
##   log10_total_counts
## colnames(268): 16cell 16cell.1 ... zy.2 zy.3
## colData names(30): cell_type2 cell_type1 ... pct_counts_ERCC
##   is_cell_control
## reducedDimNames(0):
## spikeNames(1): ERCC
## altExpNames(0):

# How many mouse cells are at each stage?
table(deng_SCE$cell_type1)

## 
## 16cell  2cell  4cell  8cell  blast zygote 
##     50     22     14     37    133     12

table(deng_SCE$cell_type2)

## 
##     16cell      4cell      8cell early2cell earlyblast  late2cell  lateblast 
##         50         14         37          8         43         10         30 
##   mid2cell   midblast         zy 
##         12         60          4

# Re-order the levels of the factor storing the cell developmental stage.
deng_SCE$cell_type2 <- factor(deng_SCE$cell_type2,
                              levels = c("zy", "early2cell", "mid2cell", "late2cell", 
                                         "4cell", "8cell", "16cell", "earlyblast",
                                         "midblast", "lateblast"))

14.3 Principle Components Analysis

Let us take a first look at the Deng data. One simple approach to ordering cells in pseudotime is to use PCA. By carrying out PCA and labeling the cells by the stage at which they were collected, we can see how well the principal components separate cells along a differentiation trajectory.

# Run PCA on Deng data. Use the runPCA function from the SingleCellExperiment package.
deng_SCE <- runPCA(deng_SCE, ncomponents = 50)

# Use the reducedDim function to access the PCA and store the results. 
pca <- reducedDim(deng_SCE, "PCA")

# Describe how the PCA is stored in a matrix. Why does it have this structure?
head(pca)

##               PC1       PC2       PC3         PC4        PC5        PC6
## 16cell   24.79868 -62.20826  8.035201 -2.07391816  2.1297390 14.0930954
## 16cell.1 28.77121 -50.35974 13.607012  0.08664449  0.9454185  3.5987880
## 16cell.2 26.67901 -61.03875  7.239352 -6.60967794 -1.0775002 11.8876579
## 16cell.3 29.01151 -56.03620  6.433057  2.85332708 -4.2885083 -0.1488504
## 16cell.4 26.38026 -58.09265  4.671850  7.99519397  9.8077416  2.0570042
## 16cell.5 24.90566 -60.77897  5.632497 -3.80156587  9.8835527 11.9028394
##                 PC7        PC8       PC9      PC10       PC11        PC12
## 16cell    2.4645020  1.6350660  7.202260  9.862212 -10.660702  -0.6401721
## 16cell.1  2.1726663 -3.3481641  8.967394  6.664942 -14.493227 -11.7471565
## 16cell.2 -7.9007309  0.3368756  6.032645  5.295515 -15.384993  -4.2930696
## 16cell.3 -4.3727592 -1.1582470  1.520145 -8.789699 -19.386866   0.4999047
## 16cell.4 -0.6031572 -3.6743278  5.793753 10.823787  -7.613724  -4.7288640
## 16cell.5 -4.3269009  3.8968881 11.805221  9.798854 -11.016137 -19.1535086
##               PC13      PC14       PC15       PC16      PC17       PC18
## 16cell   -5.716841  6.544614  -6.652210  -3.458346  4.499013 -11.360753
## 16cell.1 13.284708 -4.206404  -8.721043  -7.926277  0.703508  -5.418131
## 16cell.2  9.633173  1.672498  -9.609001  -9.302794 10.219743  -5.763834
## 16cell.3 14.177687 -8.509097  -6.978210  10.771078  6.188808   6.504081
## 16cell.4  3.106382 -4.078414 -10.739979 -12.032452  6.239499   2.331292
## 16cell.5  9.544362 -2.255400  -8.614958  -2.832196  1.798584   2.321082
##                 PC19      PC20      PC21       PC22       PC23      PC24
## 16cell     2.2617345 -2.456274 11.227414  1.7122827  -8.418641  4.254968
## 16cell.1 -11.8613891  4.069530  9.320831  0.5802347 -11.878096 -6.412425
## 16cell.2  -3.3460356  4.165813  2.031473 -2.1106373  -1.762218 -1.135134
## 16cell.3  -0.6042649  6.008176  9.982856  9.4888653   2.822138 12.871921
## 16cell.4   3.9402029 -0.298227 10.773722 -0.6374236   4.730329  4.670391
## 16cell.5  -2.0280791  5.050525 -3.252243 -7.1527175  -9.923140 -1.791511
##               PC25       PC26       PC27      PC28         PC29      PC30
## 16cell   -4.049629  -4.133374  0.6235391 -3.381254 -13.94917609  8.217824
## 16cell.1 -8.052083  -8.334263  0.5815629  4.592214  -1.32417854 -5.266909
## 16cell.2 -2.326133  -3.775858  2.3388745 -6.947394  -0.08121559  2.942813
## 16cell.3 -5.860750  -1.869659 -7.0402429  5.092207   2.53575943 18.529304
## 16cell.4 -4.291113 -13.005331 -3.2802102  4.606226   3.52531994  3.599833
## 16cell.5  4.708265  -5.717693 -1.1023767  9.761377   4.57312078 12.138646
##                PC31      PC32        PC33      PC34       PC35       PC36
## 16cell    -6.897320  5.675943   8.6076039  3.713348  0.9099737  4.7467546
## 16cell.1  -4.538307 -9.166969  -9.4525575  8.848231  2.0782319  7.4318993
## 16cell.2   3.082470  2.207176   0.5365986  3.895378 -7.4493361  0.7465149
## 16cell.3   1.680117  3.839556 -13.3156066  6.257479  4.1112596  0.2780589
## 16cell.4 -13.314741  1.453554   0.1334034 -2.941487  0.8162660 -2.9940693
## 16cell.5  -4.608498 12.180530   5.8667454 -6.645273 -1.0224859  0.8960299
##               PC37       PC38       PC39      PC40       PC41       PC42
## 16cell   -9.063470 -5.2765051 -1.1758453  9.474215  -3.559391  4.7781174
## 16cell.1 -6.217009  1.0216459 -0.5798035 21.705585   3.570104 -2.3279923
## 16cell.2 -6.227582  3.0863112 -8.6153521 -1.401230  -2.266017 -0.8150665
## 16cell.3 -8.411600  3.7169411  0.7050601  2.959623   3.123082 -1.0916370
## 16cell.4  2.871774 -4.2664023  7.4894594 -8.207422  -4.223035  1.4763577
## 16cell.5 10.169730  0.3923632  9.3346900  8.114487 -11.186021  4.5635674
##                 PC43      PC44      PC45      PC46        PC47      PC48
## 16cell   -7.92280920 -8.558202  7.058962 -3.058208  -0.5723866  4.674956
## 16cell.1  5.60067539  8.717056 -6.480960 -8.554813 -13.1868736  3.397938
## 16cell.2  5.25328812 -5.803788  2.726822 -1.241769   7.4824415 -4.088461
## 16cell.3 -0.05135523 -2.181424  2.404780 -8.691230   8.9700016 -3.713540
## 16cell.4  1.55019720  4.946841  0.520753  3.068227  10.7801148  5.167658
## 16cell.5 -9.98211745 -8.759947 -3.727758  9.064882  -1.7524456 -3.306621
##               PC49       PC50
## 16cell    2.936258  3.5978317
## 16cell.1  3.420235 -3.4895386
## 16cell.2 -4.446014 -0.2326760
## 16cell.3  5.179604  9.7144236
## 16cell.4  1.077789  3.0529018
## 16cell.5 -5.019027  0.9275007

dim(pca)

## [1] 268  50

# Add PCA data (first two PCs) to the deng_SCE object.
deng_SCE$PC1 <- pca[, 1]
deng_SCE$PC2 <- pca[, 2]
head(colData(deng_SCE))

## DataFrame with 6 rows and 32 columns
##          cell_type2  cell_type1 total_features log10_total_features
##            <factor> <character>      <integer>            <numeric>
## 16cell       16cell      16cell           7882     3.89669152656288
## 16cell.1     16cell      16cell           7671     3.88490859416261
## 16cell.2     16cell      16cell           8012     3.90379514274104
## 16cell.3     16cell      16cell           7980     3.90205731080847
## 16cell.4     16cell      16cell           8179     3.91275330367132
## 16cell.5     16cell      16cell           7291     3.86284665998294
##          total_counts log10_total_counts pct_counts_top_50_features
##             <integer>          <numeric>                  <numeric>
## 16cell        8825980   6.94576298819116           16.1419581734833
## 16cell.1      7714601   6.88731352551746           14.3400287325294
## 16cell.2      8074971   6.90714102508777           16.2521450541432
## 16cell.3      6334456    6.8017093923827           14.7442337589842
## 16cell.4      9885518   6.99499947515896           14.8676680372237
## 16cell.5     10571900   7.02415308755133           15.0683037107805
##          pct_counts_top_100_features pct_counts_top_200_features
##                            <numeric>                   <numeric>
## 16cell              22.9905574225185            31.9837570445435
## 16cell.1            20.7937779283724            29.2256333153199
## 16cell.2            23.0008380215855            32.0749387211422
## 16cell.3            21.3769738080113            30.2242213064547
## 16cell.4            21.4405557705727            29.9306015122323
## 16cell.5            21.4823636243249             30.227310133467
##          pct_counts_top_500_features total_features_endogenous
##                            <numeric>                 <integer>
## 16cell              47.7577107584654                      7882
## 16cell.1            44.9996701060755                      7671
## 16cell.2            47.7693356421961                      8012
## 16cell.3            46.1895070389628                      7980
## 16cell.4            45.5819917580444                      8179
## 16cell.5            46.3653553287489                      7291
##          log10_total_features_endogenous total_counts_endogenous
##                                <numeric>               <integer>
## 16cell                  3.89669152656288                 8825980
## 16cell.1                3.88490859416261                 7714601
## 16cell.2                3.90379514274104                 8074971
## 16cell.3                3.90205731080847                 6334456
## 16cell.4                3.91275330367132                 9885518
## 16cell.5                3.86284665998294                10571900
##          log10_total_counts_endogenous pct_counts_endogenous
##                              <numeric>             <numeric>
## 16cell                6.94576298819116                   100
## 16cell.1              6.88731352551746                   100
## 16cell.2              6.90714102508777                   100
## 16cell.3               6.8017093923827                   100
## 16cell.4              6.99499947515896                   100
## 16cell.5              7.02415308755133                   100
##          pct_counts_top_50_features_endogenous
##                                      <numeric>
## 16cell                        16.1419581734833
## 16cell.1                      14.3400287325294
## 16cell.2                      16.2521450541432
## 16cell.3                      14.7442337589842
## 16cell.4                      14.8676680372237
## 16cell.5                      15.0683037107805
##          pct_counts_top_100_features_endogenous
##                                       <numeric>
## 16cell                         22.9905574225185
## 16cell.1                       20.7937779283724
## 16cell.2                       23.0008380215855
## 16cell.3                       21.3769738080113
## 16cell.4                       21.4405557705727
## 16cell.5                       21.4823636243249
##          pct_counts_top_200_features_endogenous
##                                       <numeric>
## 16cell                         31.9837570445435
## 16cell.1                       29.2256333153199
## 16cell.2                       32.0749387211422
## 16cell.3                       30.2242213064547
## 16cell.4                       29.9306015122323
## 16cell.5                        30.227310133467
##          pct_counts_top_500_features_endogenous total_features_feature_control
##                                       <numeric>                      <integer>
## 16cell                         47.7577107584654                              0
## 16cell.1                       44.9996701060755                              0
## 16cell.2                       47.7693356421961                              0
## 16cell.3                       46.1895070389628                              0
## 16cell.4                       45.5819917580444                              0
## 16cell.5                       46.3653553287489                              0
##          log10_total_features_feature_control total_counts_feature_control
##                                     <numeric>                    <integer>
## 16cell                                      0                            0
## 16cell.1                                    0                            0
## 16cell.2                                    0                            0
## 16cell.3                                    0                            0
## 16cell.4                                    0                            0
## 16cell.5                                    0                            0
##          log10_total_counts_feature_control pct_counts_feature_control
##                                   <numeric>                  <numeric>
## 16cell                                    0                          0
## 16cell.1                                  0                          0
## 16cell.2                                  0                          0
## 16cell.3                                  0                          0
## 16cell.4                                  0                          0
## 16cell.5                                  0                          0
##          total_features_ERCC log10_total_features_ERCC total_counts_ERCC
##                    <integer>                 <numeric>         <integer>
## 16cell                     0                         0                 0
## 16cell.1                   0                         0                 0
## 16cell.2                   0                         0                 0
## 16cell.3                   0                         0                 0
## 16cell.4                   0                         0                 0
## 16cell.5                   0                         0                 0
##          log10_total_counts_ERCC pct_counts_ERCC is_cell_control
##                        <numeric>       <numeric>       <logical>
## 16cell                         0               0           FALSE
## 16cell.1                       0               0           FALSE
## 16cell.2                       0               0           FALSE
## 16cell.3                       0               0           FALSE
## 16cell.4                       0               0           FALSE
## 16cell.5                       0               0           FALSE
##                       PC1               PC2
##                 <numeric>         <numeric>
## 16cell   24.7986820262447 -62.2082648676066
## 16cell.1 28.7712069014198 -50.3597388047316
## 16cell.2 26.6790073144958 -61.0387480545727
## 16cell.3 29.0115120743145 -56.0361975940189
## 16cell.4 26.3802550037036 -58.0926458026471
## 16cell.5 24.9056588611302 -60.7789654488048

# Plot PC biplot with cells colored by cell_type2. 
# colData(deng_SCE) accesses the cell metadata DataFrame object for deng_SCE.
# Look at Figure 1A of the paper as a comparison to your PC biplot.
ggplot(as.data.frame(colData(deng_SCE)), aes(x = PC1, y = PC2, color = cell_type2)) + geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("PC1") + ylab("PC2") + ggtitle("PC biplot")

# PCA is a simple approach and can be good to compare to more complex algorithms 
# designed to capture differentiation processes. As a simple measure of pseudotime 
# we can use the coordinates of PC1.
# Plot PC1 vs cell_type2. 
deng_SCE$pseudotime_PC1 <- rank(deng_SCE$PC1)  # rank cells by their PC1 score
ggplot(as.data.frame(colData(deng_SCE)), aes(x = pseudotime_PC1, y = cell_type2, 
                                             colour = cell_type2)) +
    geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("PC1") + ylab("Timepoint") +
    ggtitle("Cells ordered by first principal component")

ggsave(paste0(mydir, "/pseudotime_PC1.png"))

## Saving 7 x 5 in image

# Try separating the cell types using other PCs. How does the separation look?
deng_SCE$PC5 <- pca[, 5]
deng_SCE$PC6 <- pca[, 6]
ggplot(as.data.frame(colData(deng_SCE)), aes(x = PC5, y = PC6, color = cell_type2)) + geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("PC5") + ylab("PC6") + ggtitle("PC biplot")

14.4 Diffusion map pseudotime

Let us see how a more advance trajectory inference method, diffusion maps and diffusion pseudotime, performs at placing cells along the expected differentiation trajectory.

Diffusion maps were introduced by Ronald Coifman and Stephane Lafon, and the underlying idea is to assume that the data are samples from a diffusion process. The method infers the low-dimensional manifold by estimating the eigenvalues and eigenvectors for the diffusion operator related to the data.

Angerer et al have applied the diffusion maps concept to the analysis of single-cell RNA-seq data to create an R package called destiny.

We will use two forms of pseudotime: the first diffusion component and the diffusion pseudotime.

#  Prepare a counts matrix with labeled rows and columns. 
deng <- logcounts(deng_SCE)  # access log-transformed counts matrix
cellLabels <- deng_SCE$cell_type2
colnames(deng) <- cellLabels

# Make a diffusion map.
dm <- DiffusionMap(t(deng))

## Warning in DiffusionMap(t(deng)): You have 22431 genes. Consider passing e.g.
## n_pcs = 50 to speed up computation.

# Optional: Try different sigma values when making diffusion map.
# dm <- DiffusionMap(t(deng), sigma = "local")  # use local option to set sigma
# sigmas <- find_sigmas(t(deng), verbose = FALSE)  # find optimal sigma
# dm <- DiffusionMap(t(deng), sigma = optimal_sigma(sigmas))  

# Plot diffusion component 1 vs diffusion component 2 (DC1 vs DC2). 
tmp <- data.frame(DC1 = eigenvectors(dm)[, 1],
                  DC2 = eigenvectors(dm)[, 2],
                  Timepoint = cellLabels)
ggplot(tmp, aes(x = DC1, y = DC2, colour = Timepoint)) +
    geom_point() + scale_color_tableau() + 
    xlab("Diffusion component 1") + 
    ylab("Diffusion component 2") +
    theme_classic()

# Try plotting higher diffusion components against one another.
tmp <- data.frame(DC3 = eigenvectors(dm)[, 3],
                  DC4 = eigenvectors(dm)[, 4],
                  Timepoint = cellLabels)
ggplot(tmp, aes(x = DC3, y = DC4, colour = Timepoint)) +
    geom_point() + #scale_color_tableau() + 
    xlab("Diffusion component 3") + 
    ylab("Diffusion component 4") +
    theme_classic()

# Next, let us use the first diffusion component (DC1) as a measure of pseudotime.
# How does the separation by cell stage look?
deng_SCE$pseudotime_diffusionmap <- rank(eigenvectors(dm)[,1])    # rank cells by their dpt
ggplot(as.data.frame(colData(deng_SCE)), 
       aes(x = pseudotime_diffusionmap, 
           y = cell_type2, colour = cell_type2)) +
    geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("Diffusion component 1 (DC1)") + ylab("Timepoint") +
    ggtitle("Cells ordered by DC1")

ggsave(paste0(mydir, "/pseudotime_DC1.png"))

## Saving 7 x 5 in image

# Plot eigenvalues of diffusion distance matrix. How many diffusion components would you use?
# This is analagous to the PC elbow plot (scree plot) that we previously used to assess how 
# many PCs to use in downstream applications like clustering.
plot(eigenvalues(dm), ylim = 0:1, pch = 20, xlab = 'Diffusion component (DC)', ylab = 'Eigenvalue')

# What happens if you run the diffusion map on the PCs? Why would one do this?
rownames(pca) <- cellLabels
dm <- DiffusionMap(pca)

# Diffusion pseudotime calculation. 
# Set index or tip of pseudotime calculation to be a zygotic cell (cell 268). 
dpt <- DPT(dm, tips = 268)

# Plot DC1 vs DC2 and color the cells by their inferred diffusion pseudotime.
# We can accesss diffusion pseudotime via dpt$dpt.
df <- data.frame(DC1 = eigenvectors(dm)[, 1], DC2 = eigenvectors(dm)[, 2], 
                 dptval = dpt$dpt, cell_type2 = cellLabels)
p1 <- ggplot(df) + geom_point(aes(x = DC1, y = DC2, color = dptval))
p2 <- ggplot(df) + geom_point(aes(x = DC1, y = DC2, color = cell_type2))
p <- plot_grid(p1, p2)
p

save_plot(paste0(mydir, "/dpt_celltype.png"), p, base_height = 5, base_aspect_ratio = 2)

# Plot diffusion pseudotime vs timepoint. 
# Which separates the data better, DC1 or diffusion pseudotime?
deng_SCE$pseudotime_dpt <- rank(dpt$dpt) 
ggplot(as.data.frame(colData(deng_SCE)), 
       aes(x = pseudotime_dpt, 
           y = cell_type2, colour = cell_type2)) +
    geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("Diffusion map pseudotime (dpt)") +
    ylab("Timepoint") +
    ggtitle("Cells ordered by diffusion map pseudotime")

ggsave(paste0(mydir, "/pseudotime_dpt.png"))

## Saving 7 x 5 in image

# Save current progress.
save(deng_SCE, file = Rda.destiny.path)
# To load the data, run the following command.
# load(Rda.destiny.path)

14.5 Slingshot map pseudotime

Let us see how another advance trajectory inference method, Slingshot, performs at placing cells along the expected differentiation trajectory.

library(slingshot)

## Loading required package: princurve

library(Seurat)

# load(Rda.destiny.path)

# Read the Slingshot documentation (?slingshot) and then run Slingshot below. 
# Given your understanding of the algorithm and the documentation, what is one 
# major set of parameters we omitted here when running Slingshot?
sce <- slingshot(deng_SCE, reducedDim = 'PCA')  # no clusters

## No cluster labels provided. Continuing with one cluster.

## Using full covariance matrix

# Plot PC1 vs PC2 colored by Slingshot pseudotime.
colors <- rainbow(50, alpha = 1)
plot(reducedDims(sce)$PCA, col = colors[cut(sce$slingPseudotime_1,breaks=50)], pch=16, asp = 1)
lines(SlingshotDataSet(sce), lwd=2)

# Plot Slingshot pseudotime vs cell stage. 
ggplot(as.data.frame(colData(deng_SCE)), aes(x = sce$slingPseudotime_1, y = cell_type2, 
                              colour = cell_type2)) +
    geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("Slingshot pseudotime") + ylab("Timepoint") +
    ggtitle("Cells ordered by Slingshot pseudotime")

# Cluster cells using the Seurat workflow below.
gcdata <- CreateSeuratObject(counts = counts(deng_SCE), project = "slingshot")

## Warning: Feature names cannot have pipe characters ('|'), replacing with dashes
## ('-')

gcdata <- NormalizeData(gcdata, normalization.method = "LogNormalize", scale.factor = 10000)
gcdata <- FindVariableFeatures(gcdata, selection.method = "vst", nfeatures = 2000)
gcdata <- ScaleData(object = gcdata, do.center = T, do.scale = F)

## Centering data matrix

gcdata <- RunPCA(gcdata, features = VariableFeatures(gcdata), npcs = 40, ndims.print = 1:5, nfeatures.print = 5)

## PC_ 1 
## Positive:  Actb, Fabp3, Psap, Akr1b8, Krt18 
## Negative:  Zbed3, C86187, Klf17, Btg4, Ccdc6 
## PC_ 2 
## Positive:  Krt18, Id2, Akr1b8, BC053393, Fabp3 
## Negative:  Gm11517, Alppl2, Obox6, Pdxk, Trim43b 
## PC_ 3 
## Positive:  Id2, Krt18, Tspan8, BC053393, Krt8 
## Negative:  Gm11517, Alppl2, Ypel5, Pdxk, Fam46c 
## PC_ 4 
## Positive:  Alppl2, Dab2, Gm11517, Krt18, Tspan8 
## Negative:  Upp1, Tdgf1, Spp1, Zfp57, Tat 
## PC_ 5 
## Positive:  Klf17, Ddx24, Bod1l, Tor1b, Gm1995 
## Negative:  Alppl2, Gm4340, Gm11756, Gm8300, Gm5039

# Cluster the cells using the first twenty principal components.
gcdata <- FindNeighbors(gcdata, reduction = "pca", dims = 1:20, k.param = 20)

## Computing nearest neighbor graph

## Computing SNN

gcdata <- FindClusters(gcdata, resolution = 0.6, algorithm = 1, random.seed = 100)

## Modularity Optimizer version 1.3.0 by Ludo Waltman and Nees Jan van Eck
## 
## Number of nodes: 268
## Number of edges: 6804
## 
## Running Louvain algorithm...
## Maximum modularity in 10 random starts: 0.8081
## Number of communities: 5
## Elapsed time: 0 seconds

# Add clustering information from Seurat to the deng_SCE object
deng_SCE$slingPseudotime_1 <- NULL  # remove old slingshot pseudotime data
colData(deng_SCE)$Seurat_clusters <- as.character(Idents(gcdata))  # go from factor to character
head(colData(deng_SCE))

## DataFrame with 6 rows and 38 columns
##          cell_type2  cell_type1 total_features log10_total_features
##            <factor> <character>      <integer>            <numeric>
## 16cell       16cell      16cell           7882     3.89669152656288
## 16cell.1     16cell      16cell           7671     3.88490859416261
## 16cell.2     16cell      16cell           8012     3.90379514274104
## 16cell.3     16cell      16cell           7980     3.90205731080847
## 16cell.4     16cell      16cell           8179     3.91275330367132
## 16cell.5     16cell      16cell           7291     3.86284665998294
##          total_counts log10_total_counts pct_counts_top_50_features
##             <integer>          <numeric>                  <numeric>
## 16cell        8825980   6.94576298819116           16.1419581734833
## 16cell.1      7714601   6.88731352551746           14.3400287325294
## 16cell.2      8074971   6.90714102508777           16.2521450541432
## 16cell.3      6334456    6.8017093923827           14.7442337589842
## 16cell.4      9885518   6.99499947515896           14.8676680372237
## 16cell.5     10571900   7.02415308755133           15.0683037107805
##          pct_counts_top_100_features pct_counts_top_200_features
##                            <numeric>                   <numeric>
## 16cell              22.9905574225185            31.9837570445435
## 16cell.1            20.7937779283724            29.2256333153199
## 16cell.2            23.0008380215855            32.0749387211422
## 16cell.3            21.3769738080113            30.2242213064547
## 16cell.4            21.4405557705727            29.9306015122323
## 16cell.5            21.4823636243249             30.227310133467
##          pct_counts_top_500_features total_features_endogenous
##                            <numeric>                 <integer>
## 16cell              47.7577107584654                      7882
## 16cell.1            44.9996701060755                      7671
## 16cell.2            47.7693356421961                      8012
## 16cell.3            46.1895070389628                      7980
## 16cell.4            45.5819917580444                      8179
## 16cell.5            46.3653553287489                      7291
##          log10_total_features_endogenous total_counts_endogenous
##                                <numeric>               <integer>
## 16cell                  3.89669152656288                 8825980
## 16cell.1                3.88490859416261                 7714601
## 16cell.2                3.90379514274104                 8074971
## 16cell.3                3.90205731080847                 6334456
## 16cell.4                3.91275330367132                 9885518
## 16cell.5                3.86284665998294                10571900
##          log10_total_counts_endogenous pct_counts_endogenous
##                              <numeric>             <numeric>
## 16cell                6.94576298819116                   100
## 16cell.1              6.88731352551746                   100
## 16cell.2              6.90714102508777                   100
## 16cell.3               6.8017093923827                   100
## 16cell.4              6.99499947515896                   100
## 16cell.5              7.02415308755133                   100
##          pct_counts_top_50_features_endogenous
##                                      <numeric>
## 16cell                        16.1419581734833
## 16cell.1                      14.3400287325294
## 16cell.2                      16.2521450541432
## 16cell.3                      14.7442337589842
## 16cell.4                      14.8676680372237
## 16cell.5                      15.0683037107805
##          pct_counts_top_100_features_endogenous
##                                       <numeric>
## 16cell                         22.9905574225185
## 16cell.1                       20.7937779283724
## 16cell.2                       23.0008380215855
## 16cell.3                       21.3769738080113
## 16cell.4                       21.4405557705727
## 16cell.5                       21.4823636243249
##          pct_counts_top_200_features_endogenous
##                                       <numeric>
## 16cell                         31.9837570445435
## 16cell.1                       29.2256333153199
## 16cell.2                       32.0749387211422
## 16cell.3                       30.2242213064547
## 16cell.4                       29.9306015122323
## 16cell.5                        30.227310133467
##          pct_counts_top_500_features_endogenous total_features_feature_control
##                                       <numeric>                      <integer>
## 16cell                         47.7577107584654                              0
## 16cell.1                       44.9996701060755                              0
## 16cell.2                       47.7693356421961                              0
## 16cell.3                       46.1895070389628                              0
## 16cell.4                       45.5819917580444                              0
## 16cell.5                       46.3653553287489                              0
##          log10_total_features_feature_control total_counts_feature_control
##                                     <numeric>                    <integer>
## 16cell                                      0                            0
## 16cell.1                                    0                            0
## 16cell.2                                    0                            0
## 16cell.3                                    0                            0
## 16cell.4                                    0                            0
## 16cell.5                                    0                            0
##          log10_total_counts_feature_control pct_counts_feature_control
##                                   <numeric>                  <numeric>
## 16cell                                    0                          0
## 16cell.1                                  0                          0
## 16cell.2                                  0                          0
## 16cell.3                                  0                          0
## 16cell.4                                  0                          0
## 16cell.5                                  0                          0
##          total_features_ERCC log10_total_features_ERCC total_counts_ERCC
##                    <integer>                 <numeric>         <integer>
## 16cell                     0                         0                 0
## 16cell.1                   0                         0                 0
## 16cell.2                   0                         0                 0
## 16cell.3                   0                         0                 0
## 16cell.4                   0                         0                 0
## 16cell.5                   0                         0                 0
##          log10_total_counts_ERCC pct_counts_ERCC is_cell_control
##                        <numeric>       <numeric>       <logical>
## 16cell                         0               0           FALSE
## 16cell.1                       0               0           FALSE
## 16cell.2                       0               0           FALSE
## 16cell.3                       0               0           FALSE
## 16cell.4                       0               0           FALSE
## 16cell.5                       0               0           FALSE
##                       PC1               PC2 pseudotime_PC1               PC5
##                 <numeric>         <numeric>      <numeric>         <numeric>
## 16cell   24.7986820262447 -62.2082648676066            171  2.12973902514438
## 16cell.1 28.7712069014198 -50.3597388047316            181 0.945418456955433
## 16cell.2 26.6790073144958 -61.0387480545727            176 -1.07750020611762
## 16cell.3 29.0115120743145 -56.0361975940189            183 -4.28850833105763
## 16cell.4 26.3802550037036 -58.0926458026471            175  9.80774159539532
## 16cell.5 24.9056588611302 -60.7789654488048            172  9.88355269770382
##                         PC6 pseudotime_diffusionmap pseudotime_dpt
##                   <numeric>               <numeric>      <numeric>
## 16cell     14.0930954146809                     123             88
## 16cell.1   3.59878801496069                     182             68
## 16cell.2   11.8876579313426                     122            122
## 16cell.3 -0.148850434153179                     173             74
## 16cell.4   2.05700416962238                     128            102
## 16cell.5   11.9028394497909                     144             63
##          Seurat_clusters
##              <character>
## 16cell                 0
## 16cell.1               0
## 16cell.2               0
## 16cell.3               0
## 16cell.4               0
## 16cell.5               0

# Then run Slingshot using these cluster assignments.
deng_SCE <- slingshot(deng_SCE, clusterLabels = 'Seurat_clusters', reducedDim = 'PCA')

## Using diagonal covariance matrix

# Plot PC1 vs PC2 colored by Slingshot pseudotime.
colors <- rainbow(50, alpha = 1)
plot(reducedDims(deng_SCE)$PCA, col = colors[cut(deng_SCE$slingPseudotime_1,breaks=50)], pch=16, asp = 1)
lines(SlingshotDataSet(deng_SCE), lwd=2)

# Plot Slingshot pseudotime vs cell stage. 
ggplot(as.data.frame(colData(deng_SCE)), aes(x = slingPseudotime_1, y = cell_type2, 
                              colour = cell_type2)) +
    geom_quasirandom(groupOnX = FALSE) +
    scale_color_tableau() + theme_classic() +
    xlab("Slingshot pseudotime") + ylab("Timepoint") +
    ggtitle("Cells ordered by Slingshot pseudotime")

## Warning: Removed 24 rows containing missing values (position_quasirandom).

ggsave(paste0(mydir, "/pseudotime_slingshot.png"))

## Saving 7 x 5 in image

## Warning: Removed 24 rows containing missing values (position_quasirandom).

# Save current progress.
save(deng_SCE, file = Rda.slingshot.path)
# To load the data, run the following command.
# load(Rda.slingshot.path)

14.6 Find temporally expressed genes

In this final analysis code chunk, we will identify temporally expressed genes, ie those genes whose expression is changing in a continuous manner over pseudotime. To do this, we will fit a GAM with a LOESS term for pseudotime. Functions for fitting and working with generalized additive models, as described in “Generalized Additive Models” (Hastie and Tibshirani, 1990). Read more about GAMs

# Only look at the 1,000 most variable genes when identifying temporally expressesd genes.
# Identify the variable genes by ranking all genes by their variance.
Y <- log2(counts(deng_SCE) + 1)
var1K <- names(sort(apply(Y, 1, var), decreasing = TRUE))[1:1000]
Y <- Y[var1K, ]  # only counts for variable genes

# Fit GAM for each gene using pseudotime as independent variable.
t <- deng_SCE$slingPseudotime_1
gam.pval <- apply(Y, 1, function(z){
  d <- data.frame(z=z, t=t)
  tmp <- gam(z ~ lo(t), data=d)
  p <- summary(tmp)[4][[1]][1,5]
  p
})

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

## Warning in model.matrix.default(mt, mf, contrasts): non-list contrasts argument
## ignored

# Identify genes with the most significant time-dependent model fit.
topgenes <- names(sort(gam.pval, decreasing = FALSE))[1:100]  

# Prepare and plot a heatmap of the top genes that vary their expression over pseudotime.
require(clusterExperiment)
heatdata <- as.matrix(gcdata[['RNA']]@data[rownames(gcdata) %in% topgenes, order(t, na.last = NA)])
heatclus <- Idents(gcdata)[order(t, na.last = NA)]
png(paste0(mydir, "heatmap_time_genes.png"), width=10, height=10, units = "in", res=200)
# ce <- ClusterExperiment(heatdata, heatclus, transformation = log1p)
# clusterExperiment::plotHeatmap(ce, clusterSamplesData = "orderSamplesValue", visualizeData = 'transformed', cexRow = 1.5, fontsize = 15)
heatmap(log1p(heatdata), Colv = NA, ColSideColors = brewer.pal(9,"Set1")[heatclus])
dev.off()

## png 
##   2

14.7 Comparison of the different trajectory inference methods

How do the trajectories inferred by PCA, diffusion pseudotime, and slingshot pseudotime compare to one another?

# Prepare data frame with different pseudotime measures.
df_pseudotime <- as.data.frame(colData(deng_SCE)[, c("pseudotime_PC1", "pseudotime_dpt", "slingPseudotime_1")])
colnames(df_pseudotime) <- c("PC1", "diffusion", "slingshot")

# Plot correlation between different pseudotime measures.
corrplot.mixed(cor(df_pseudotime, use = "na.or.complete"), 
               order = "hclust", tl.col = "black",
               main = "Correlation matrix for pseudotime results",
               mar = c(0, 0, 3.1, 0))

14.8 Plots of gene expression over time.

Visualize how some of the temporally expressed genes change in time.

plotExpression(deng_SCE, "Obox5", x = "PC1", 
               colour_by = "cell_type2", show_violin = FALSE,
               show_smooth = TRUE)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plotExpression(deng_SCE, "Obox5", x = "pseudotime_dpt", 
               colour_by = "cell_type2", show_violin = FALSE,
               show_smooth = TRUE)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

plotExpression(deng_SCE, "Obox5", x = "slingPseudotime_1", 
               colour_by = "cell_type2", show_violin = FALSE,
               show_smooth = TRUE)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

## Warning: Removed 24 rows containing non-finite values (stat_smooth).

## Warning: Removed 24 rows containing missing values (geom_point).

14.9 Acknowledgements

This document builds off chapter 8.4 from the Analysis of single cell RNA-seq data, from the Destiny vignette and from the Slingshot vignette.