Motif and gene analysis using topic modeling results for Buenrostro et al (2018) scATAC-seq result (data processed using Chen 2019 pipeline)

Last updated: 2021-01-05

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Knit directory: scATACseq-topics/

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File	Version	Author	Date	Message
Rmd	7873cd2	kevinlkx	2021-01-05	fixed an issue with the gene score results and added motif results using top 2000 regions
html	1b9daa1	kevinlkx	2020-12-23	Build site.
Rmd	ca7b282	kevinlkx	2020-12-23	wflow_publish("motif_gene_analysis_Buenrostro2018_Chen2019pipeline.Rmd")
html	652b265	kevinlkx	2020-12-23	Build site.
Rmd	2886256	kevinlkx	2020-12-23	motif and gene analysis for Buenrostro 2018 result with data processed using Chen 2019 pipeline

Here we perform TF motif and gene analysis for the Buenrostro et al (2018) scATAC-seq result inferred from the multinomial topic model with \(k = 11\).

We use binarized scPeaks and scATAC-seq data was processed using Chen et al (2019) pipeline.

Load packages and some functions used in this analysis

library(Matrix)
library(dplyr)
library(ggplot2)
library(cowplot)
library(fastTopics)
library(dplyr)
library(tidyr)
library(DT)
library(reshape)

Load data and topic model results

Load the binarized data and the \(k = 11\) Poisson NMF fit results

data.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/data/Buenrostro_2018/processed_data_Chen2019pipeline/"
load(file.path(data.dir, "Buenrostro_2018_binarized_counts.RData"))

fit.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized/"
fit <- readRDS(file.path(fit.dir, "/fit-Buenrostro2018-binarized-scd-ex-k=11.rds"))$fit
fit_multinom <- poisson2multinom(fit)

Visualize by Structure plot grouped by cell labels.

set.seed(10)
colors_topics <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c",
                   "#fdbf6f","#ff7f00","#cab2d6","#6a3d9a","#ffff99","#b15928",
                   "gray")
samples$label <- as.factor(samples$label)

p.structure <- structure_plot(fit_multinom,
                     grouping = samples[, "label"],n = Inf,gap = 40,
                     perplexity = 50,topics = 1:11,colors = colors_topics,
                     num_threads = 4,verbose = FALSE)
# Perplexity automatically changed to 24 because original setting of 50 was too large for the number of samples (78)
# Perplexity automatically changed to 44 because original setting of 50 was too large for the number of samples (138)
# Perplexity automatically changed to 20 because original setting of 50 was too large for the number of samples (64)
# Perplexity automatically changed to 46 because original setting of 50 was too large for the number of samples (142)
# Perplexity automatically changed to 45 because original setting of 50 was too large for the number of samples (141)
# Perplexity automatically changed to 18 because original setting of 50 was too large for the number of samples (60)

print(p.structure)

Version	Author	Date
652b265	kevinlkx	2020-12-23

Differential accessbility analysis of the ATAC-seq regions for the topics

out.dir <- "/project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized/"
diffcount_file <- file.path(out.dir, "diffcount-Buenrostro2018-11topics.rds")
if(file.exists(diffcount_file)){
  cat("Load precomputed differential accessbility statistics.\n")
  diff_count_topics <- readRDS(diffcount_file)
}else{
  cat("Computing differential accessbility statistics from topic model.\n")
  timing <- system.time(diff_count_topics <- diff_count_analysis(fit,counts))
  cat(sprintf("Computation took %0.2f seconds.\n",timing["elapsed"]))
  cat("Saving results.\n")
  saveRDS(diff_count_topics, diffcount_file)
}
# Load precomputed differential accessbility statistics.

Distribution of z-scores


zscore_topics <-  melt(diff_count_topics$Z)
colnames(zscore_topics) <- c("region", "topic", "zscore")
levels(zscore_topics$topic) <- colnames(diff_count_topics$Z)

z.quantile.99 <- apply(abs(diff_count_topics$Z), 2, quantile, 0.99)
cat("z-score 99% quantile: \n")
print(z.quantile.99)

p.hist.zscores <- ggplot(zscore_topics, aes(x=zscore)) + 
  geom_histogram(binwidth=1, color="black", fill="white") + 
  coord_cartesian(xlim = c(-10, 20)) + theme_cowplot(font_size = 10) +
  facet_wrap(~ topic, ncol=4)

print(p.hist.zscores)

Version	Author	Date
652b265	kevinlkx	2020-12-23

# z-score 99% quantile: 
#        k1        k2        k3        k4        k5        k6        k7        k8 
#  7.680613  7.226323  5.954049 10.059326  9.203917  5.821598  7.215842  8.156498 
#        k9       k10       k11 
#  5.978363  6.684635  8.191629

Motif enrichment analysis using HOMER

Details about HOMER motif analysis:
- http://homer.ucsd.edu/homer/motif/
- http://homer.ucsd.edu/homer/ngs/peakMotifs.html
Motif enrichment result using regions with z-score above 99% quantile.

homer.dir <- paste0(out.dir, "/motifanalysis-Buenrostro2018-k=11-quantile/HOMER/")
cat(sprintf("Directory of motif analysis result: %s \n", homer.dir))
homer_res <- readRDS(file.path(homer.dir, "/homer_knownResults.rds"))
selected_regions <- readRDS(file.path(homer.dir, "/selected_regions.rds"))

cat("Number of regions selected for each topic: \n")
print(mapply(nrow, selected_regions[1:(length(selected_regions)-1)]))

top_motifs <- data.frame(matrix(nrow=10, ncol = ncol(diff_count_topics$Z)))
colnames(top_motifs) <- colnames(diff_count_topics$Z)
for (k in colnames(top_motifs)){
  homer_motifs <- homer_res[[k]]
  colnames(homer_motifs) <- c("Motif.name", "Consensus", "P-value", "Log.P-value", "q-value (Benjamini)", 
                              "# of Target Sequences with Motif", "% of Target Sequences with Motif",
                              "# of Background Sequences with Motif", "% of Background Sequences with Motif")
  homer_motifs <- homer_motifs %>% separate(Motif.name, c("motif", "experiment", "database"), "/")
  top_motifs[,k] <- head(homer_motifs$motif, 10)
}

DT::datatable(data.frame(rank = 1:10, top_motifs), rownames = F,
              caption = "Top 10 motifs enriched in each topic.")
# Directory of motif analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//motifanalysis-Buenrostro2018-k=11-quantile/HOMER/ 
# Number of regions selected for each topic: 
#   k1   k2   k3   k4   k5   k6   k7   k8   k9  k10  k11 
# 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012 1012

Motif enrichment result using regions with top 2000 regions with the highest z-score.

homer.dir <- paste0(out.dir, "/motifanalysis-Buenrostro2018-k=11-topN/HOMER/")
cat(sprintf("Directory of motif analysis result: %s \n", homer.dir))
homer_res <- readRDS(file.path(homer.dir, "/homer_knownResults.rds"))
selected_regions <- readRDS(file.path(homer.dir, "/selected_regions.rds"))

cat("Number of regions selected for each topic: \n")
print(mapply(nrow, selected_regions[1:(length(selected_regions)-1)]))

top_motifs <- data.frame(matrix(nrow=10, ncol = ncol(diff_count_topics$Z)))
colnames(top_motifs) <- colnames(diff_count_topics$Z)
for (k in colnames(top_motifs)){
  homer_motifs <- homer_res[[k]]
  colnames(homer_motifs) <- c("Motif.name", "Consensus", "P-value", "Log.P-value", "q-value (Benjamini)", 
                              "# of Target Sequences with Motif", "% of Target Sequences with Motif",
                              "# of Background Sequences with Motif", "% of Background Sequences with Motif")
  homer_motifs <- homer_motifs %>% separate(Motif.name, c("motif", "experiment", "database"), "/")
  top_motifs[,k] <- head(homer_motifs$motif, 10)
}

DT::datatable(data.frame(rank = 1:10, top_motifs), rownames = F,
              caption = "Top 10 motifs enriched in each topic.")
# Directory of motif analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//motifanalysis-Buenrostro2018-k=11-topN/HOMER/ 
# Number of regions selected for each topic: 
#   k1   k2   k3   k4   k5   k6   k7   k8   k9  k10  k11 
# 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000

Top genes

Gene body model

Gene scores were computed using the gene score model (model 42) in the archR paper with some modifications. This model uses bi-directional exponential decays from the gene TSS (extended upstream by 5 kb by default) and the gene transcription termination site (TTS). Note: the current version of the function does not account for neighboring gene boundaries.

Gene body model, normalized by the l2 norm of weights, as in Stouffer's z-score method.

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)

rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]

for (k in colnames(top_genes)){
  top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}

DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
              caption = "Top 10 genes in each topic.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-genebody-l2

Gene body model, normalized by the total weights (i.e. weighted averge).

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)

rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]

for (k in colnames(top_genes)){
  top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}

DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
              caption = "Top 10 genes in each topic.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-genebody-sum

TSS model

Gene scores were computed using TSS based method as in Lareau et al. Nature Biotech, 2019 as well as the model 21 in archR paper. This model weights chromatin accessibility around gene promoters by using bi-directional exponential decays from the TSS.

TSS model, normalized by the l2 norm of weights, as in Stouffer's z-score method.

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)

rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]

for (k in colnames(top_genes)){
  top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}

DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
              caption = "Top 10 genes in each topic.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-TSS-l2

TSS model, normalized by the total weights (i.e. weighted averge).

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)

rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]

for (k in colnames(top_genes)){
  top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}

DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
              caption = "Top 10 genes in each topic.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-TSS-sum

Gene-set enrichment analysis (GSEA)

Gene body model, normalized by the l2 norm of weights, as in Stouffer's z-score method.

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)

for (k in 1:ncol(gsea_res$pval)){
  gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),  
                           pval = gsea_res$pval[,k],
                           log2err = gsea_res$log2err[,k],
                           ES = gsea_res$ES[,k],
                           NES = gsea_res$NES[,k])
  gsea_up <- gsea_topic[gsea_topic$ES > 0,]
  top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
  top_pathways_up[,k] <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")] %>% 
                     unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
  
  gsea_down <- gsea_topic[gsea_topic$ES < 0,]
  top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
  top_pathways_down[,k] <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")] %>% 
                     unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
}

DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
              caption = "Top 10 pathways enriched at the top of the gene rank list.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-genebody-l2

Gene body model, normalized by the total weights (i.e. weighted averge).

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)

for (k in 1:ncol(gsea_res$pval)){
  gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),  
                           pval = gsea_res$pval[,k],
                           log2err = gsea_res$log2err[,k],
                           ES = gsea_res$ES[,k],
                           NES = gsea_res$NES[,k])
  gsea_up <- gsea_topic[gsea_topic$ES > 0,]
  top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
  top_pathways_up[,k] <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")] %>% 
                     unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
  
  gsea_down <- gsea_topic[gsea_topic$ES < 0,]
  top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
  top_pathways_down[,k] <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")] %>% 
                     unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
}

DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
              caption = "Top 10 pathways enriched at the top of the gene rank list.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-genebody-sum

TSS model, normalized by the l2 norm of weights, as in Stouffer's z-score method.

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)

for (k in 1:ncol(gsea_res$pval)){
  gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),  
                           pval = gsea_res$pval[,k],
                           log2err = gsea_res$log2err[,k],
                           ES = gsea_res$ES[,k],
                           NES = gsea_res$NES[,k])
  gsea_up <- gsea_topic[gsea_topic$ES > 0,]
  top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
  top_IDs_up <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")]
  top_pathways_up[,k] <- paste0(top_IDs_up$name, "(", top_IDs_up$id, ")")
  
  gsea_down <- gsea_topic[gsea_topic$ES < 0,]
  top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
  top_IDs_down <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")]
  top_pathways_down[,k] <- paste0(top_IDs_down$name, "(", top_IDs_down$id, ")")
  
}

DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
              caption = "Top 10 pathways enriched at the top of the gene rank list.")
# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-TSS-l2

TSS model, normalized by the total weights (i.e. weighted averge).

gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))

top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)

for (k in 1:ncol(gsea_res$pval)){
  gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),  
                           pval = gsea_res$pval[,k],
                           log2err = gsea_res$log2err[,k],
                           ES = gsea_res$ES[,k],
                           NES = gsea_res$NES[,k])
  gsea_up <- gsea_topic[gsea_topic$ES > 0,]
  top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
  top_IDs_up <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")]
  top_pathways_up[,k] <- paste0(top_IDs_up$name, "(", top_IDs_up$id, ")")
  
  gsea_down <- gsea_topic[gsea_topic$ES < 0,]
  top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
  top_IDs_down <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")]
  top_pathways_down[,k] <- paste0(top_IDs_down$name, "(", top_IDs_down$id, ")")
  
}

DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
              caption = "Top 10 pathways enriched at the top of the gene rank list.")

# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_Chen2019pipeline/binarized//geneanalysis-Buenrostro2018-k=11-TSS-sum

sessionInfo()
# R version 3.6.1 (2019-07-05)
# Platform: x86_64-pc-linux-gnu (64-bit)
# Running under: Scientific Linux 7.4 (Nitrogen)
# 
# Matrix products: default
# BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
# 
# locale:
#  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
# [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] reshape_0.8.8    DT_0.16          tidyr_1.1.2      fastTopics_0.4-6
# [5] cowplot_1.1.0    ggplot2_3.3.2    dplyr_1.0.2      Matrix_1.2-18   
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0      Rcpp_1.0.5         lattice_0.20-41    prettyunits_1.1.1 
#  [5] rprojroot_2.0.2    digest_0.6.27      plyr_1.8.6         R6_2.5.0          
#  [9] MatrixModels_0.4-1 evaluate_0.14      coda_0.19-4        httr_1.4.2        
# [13] pillar_1.4.7       rlang_0.4.9        progress_1.2.2     lazyeval_0.2.2    
# [17] data.table_1.13.4  irlba_2.3.3        SparseM_1.78       whisker_0.4       
# [21] rmarkdown_2.6      labeling_0.4.2     Rtsne_0.15         stringr_1.4.0     
# [25] htmlwidgets_1.5.3  munsell_0.5.0      compiler_3.6.1     httpuv_1.5.4      
# [29] xfun_0.19          pkgconfig_2.0.3    mcmc_0.9-7         htmltools_0.5.0   
# [33] tidyselect_1.1.0   tibble_3.0.4       workflowr_1.6.2    quadprog_1.5-8    
# [37] matrixStats_0.57.0 viridisLite_0.3.0  crayon_1.3.4       conquer_1.0.2     
# [41] withr_2.3.0        later_1.1.0.1      MASS_7.3-53        grid_3.6.1        
# [45] jsonlite_1.7.2     gtable_0.3.0       lifecycle_0.2.0    git2r_0.27.1      
# [49] magrittr_2.0.1     scales_1.1.1       RcppParallel_5.0.2 stringi_1.5.3     
# [53] farver_2.0.3       fs_1.3.1           promises_1.1.1     ellipsis_0.3.1    
# [57] generics_0.1.0     vctrs_0.3.6        tools_3.6.1        glue_1.4.2        
# [61] purrr_0.3.4        crosstalk_1.1.0.1  hms_0.5.3          yaml_2.2.1        
# [65] colorspace_2.0-0   plotly_4.9.2.1     knitr_1.30         quantreg_5.75     
# [69] MCMCpack_1.4-9