Last updated: 2020-05-02

Checks: 7 0

Knit directory: social_immunity/

This reproducible R Markdown analysis was created with workflowr (version 1.6.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.


Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

The command set.seed(20191017) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version f188968. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:


Ignored files:
    Ignored:    .DS_Store
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    code/notes from old analysis of movement.R
    Ignored:    data/.DS_Store
    Ignored:    data/movement data - not used/
    Ignored:    output/exp1_model.rds
    Ignored:    output/exp1_post_prob.rds
    Ignored:    output/exp2_model.rds
    Ignored:    output/exp2_post_prob.rds
    Ignored:    output/exp3_model.rds
    Ignored:    output/exp3_post_prob.rds

Unstaged changes:
    Modified:   .gitignore
    Modified:   figures/fig1.pdf
    Modified:   figures/fig2.pdf

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.


These are the previous versions of the repository in which changes were made to the R Markdown (analysis/experiment3.Rmd) and HTML (docs/experiment3.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
Rmd f188968 lukeholman 2020-05-02 tweak colours
html f188968 lukeholman 2020-05-02 tweak colours
html 2227713 lukeholman 2020-05-02 Build site.
html 1c9a1c3 lukeholman 2020-05-02 Build site.
Rmd 3d21d6a lukeholman 2020-05-02 wflow_publish("*", republish = T)
html 3d21d6a lukeholman 2020-05-02 wflow_publish("*", republish = T)
html d56c18f lukeholman 2020-04-30 Build site.
Rmd c895d8d lukeholman 2020-04-30 new font
html 93c487a lukeholman 2020-04-30 Build site.
html 5c45197 lukeholman 2020-04-30 Build site.
html 4bd75dc lukeholman 2020-04-30 Build site.
Rmd 12953af lukeholman 2020-04-30 test new theme
html d6437a5 lukeholman 2020-04-25 Build site.
html e58e720 lukeholman 2020-04-25 Build site.
html 71b6160 lukeholman 2020-04-25 Build site.
Rmd 76a317d lukeholman 2020-04-25 tweaks
html 2235ae4 lukeholman 2020-04-25 Build site.
Rmd 99649a7 lukeholman 2020-04-25 tweaks
html 99649a7 lukeholman 2020-04-25 tweaks
html 0ede6e3 lukeholman 2020-04-24 Build site.
Rmd a1f8dc2 lukeholman 2020-04-24 tweaks
html a1f8dc2 lukeholman 2020-04-24 tweaks
html 8c3b471 lukeholman 2020-04-21 Build site.
Rmd 1ce9e19 lukeholman 2020-04-21 First commit 2020
html 1ce9e19 lukeholman 2020-04-21 First commit 2020
Rmd aae65cf lukeholman 2019-10-17 First commit
html aae65cf lukeholman 2019-10-17 First commit

Load data and R packages

# All but 1 of these packages can be easily installed from CRAN.
# However it was harder to install the showtext package. On Mac, I did this:
# installed 'homebrew' using Terminal: ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)" 
# installed 'libpng' using Terminal: brew install libpng
# installed 'showtext' in R using: devtools::install_github("yixuan/showtext")  
library(showtext)

library(brms)
library(bayesplot)
library(tidyverse)
library(gridExtra)
library(kableExtra)
library(bayestestR)
library(cowplot)
library(tidybayes)
library(scales)
source("code/helper_functions.R")

# set up nice font for figure
nice_font <- "Lora"
font_add_google(name = nice_font, family = nice_font, regular.wt = 400, bold.wt = 700)
showtext_auto()

files <- c("data/data_collection_sheets/hiveA_touching.csv",
           "data/data_collection_sheets/hiveB_touching.csv",
           "data/data_collection_sheets/hiveC_touching.csv",
           "data/data_collection_sheets/hiveD_touching.csv")

experiment3 <- map(
  files, 
  ~ read_csv(.x) %>%
    gather(minute, touching, -tube) %>%
    mutate(treatment = ifelse(substr(tube, 1, 1) %in% c("A", "B"), "AB", "CD"),
           minute = as.numeric(minute),
           touching = as.integer(touching),
           hive = gsub("hive", "", str_extract(.x, "hive[ABCD]")), 
           tube = paste(hive, tube, sep = "_"))
  ) %>% bind_rows() %>%
  mutate(treatment = replace(treatment, 
                             treatment == "AB" & hive %in% c("A", "B"), 
                             "Ringers"),
         treatment = replace(treatment, 
                             treatment == "AB" & hive %in% c("C", "D"), 
                             "LPS"),
         treatment = replace(treatment, 
                             treatment == "CD" & hive %in% c("A", "B"), 
                             "LPS"),
         treatment = replace(treatment, 
                             treatment == "CD" & hive %in% c("C", "D"), 
                             "Ringers")) %>%
  mutate(hive = replace(hive, hive == "A", "Garden"),
         hive = replace(hive, hive == "B", "Skylab"),
         hive = replace(hive, hive == "C", "Arts"),
         hive = replace(hive, hive == "D", "Zoology")) %>%
  rename(pairID = tube)


expt3_counts <- experiment3 %>%
  group_by(treatment, pairID, hive) %>%
  summarise(n_touching = sum(touching),
            n_not_touching = sum(touching== 0),
            percent = n_touching / (n_touching + n_not_touching)) %>% 
  ungroup() %>%
  filter(!is.na(n_touching)) %>%
  mutate(treatment = factor(treatment, c("Ringers", "LPS"))) %>%
  mutate(hive = C(factor(hive), sum)) # sum coding for hive
time <- experiment3 %>%
  group_by(treatment, hive, minute) %>%
  summarise(n = sum(touching),
            total = n(),
            prop = n / total) 

time %>%
  ggplot(aes(minute, prop, colour = treatment))  +
  geom_line() +
  facet_wrap(~ hive)

library(lme4)
repeated <- brm(touching ~ treatment * hive * minute + (minute | pairID), 
                prior = prior(normal(0, 1.5), class = "b"),
                iter = 4000, 
                data = experiment3 %>%
                  mutate(minute = as.numeric(scale(minute))), family = "bernoulli")

new <- experiment3 %>%
  mutate(minute = as.numeric(scale(minute))) %>%
  select(hive, treatment, minute) %>% distinct()
data.frame(new, pred=predict(gam_model, newdata = new, re.form = NA, type = "response", se.fit =T)) %>%
  ggplot(aes(minute, pred, colour = treatment))  +
  geom_line() +
  facet_wrap(~ hive)

Inspect the raw data

Sample sizes by treatment

sample_sizes <- expt3_counts %>%
  group_by(treatment) %>%
  summarise(n = n()) 

sample_sizes %>%
  kable() %>% kable_styling(full_width = FALSE)
treatment n
Ringers 220
LPS 219

Sample sizes by treatment and hive

expt3_counts %>%
  group_by(hive, treatment) %>%
  summarise(n = n()) %>%
  kable() %>% kable_styling(full_width = FALSE)
hive treatment n
Arts Ringers 50
Arts LPS 50
Garden Ringers 70
Garden LPS 70
Skylab Ringers 50
Skylab LPS 49
Zoology Ringers 50
Zoology LPS 50

Means and standard errors

expt3_counts %>%
  group_by(hive, treatment) %>%
  summarise(pc = mean(100 * percent),
            SE = sd(percent) /sqrt(n()),
            n = n()) %>%
  rename(`% observations in which bees were in close contact` = pc,
         Hive = hive, Treatment = treatment) %>% 
  kable(digits = 3) %>% kable_styling(full_width = FALSE) %>%
  column_spec(3, width = "2in")
Hive Treatment % observations in which bees were in close contact SE n
Arts Ringers 69.509 0.036 50
Arts LPS 72.547 0.033 50
Garden Ringers 76.752 0.033 70
Garden LPS 68.895 0.037 70
Skylab Ringers 70.509 0.040 50
Skylab LPS 65.653 0.034 49
Zoology Ringers 84.075 0.021 50
Zoology LPS 73.019 0.037 50

Histogram of the results

Note that bees more often spent close to 100% of the observation period in contact in the control group, relative to the group treated with LPS.

histo_data <- expt3_counts %>%
  left_join(sample_sizes, by = "treatment") %>%
  arrange(treatment) %>%
  mutate(treatment = factor(paste(treatment, " (n = ", n, ")", sep = ""),
                            unique(paste(treatment, " (n = ", n, ")", sep = "")))) 

raw_histogram <- histo_data %>% 
  filter(grepl("Ringers", treatment)) %>%
  ggplot(aes(100 * percent, 
             fill = treatment)) + 
  geom_histogram(data = histo_data %>% 
                   filter(grepl("LPS", treatment)), 
                 mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, colour = "black", linetype = 2) +
  geom_histogram(mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, 
                 colour = "black") + 
  scale_fill_brewer(palette = "Set1", 
                    direction = 1, name = "Treatment") + 
  xlab("% Time in close contact") + ylab("Density") + 
  theme_bw() + 
  theme(legend.position = c(0.37, 0.832),
        legend.background = element_rect(fill = scales::alpha('white', 0.7)),
        text = element_text(family = nice_font)) 

rm(histo_data)
raw_histogram

Version Author Date
f188968 lukeholman 2020-05-02
8c3b471 lukeholman 2020-04-21
aae65cf lukeholman 2019-10-17

Binomial model of time spent in contact

Run the models

Fit three different binomial models, where the response is either a 0 (if bees were not in contact) or 1 (if they were).

if(!file.exists("output/exp3_model.rds")){
  exp3_model_v1 <- brm(
    n_touching | trials(n) ~ treatment * hive + (1 | pairID), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  exp3_model_v2 <- brm(
    n_touching | trials(n) ~ treatment + hive + (1 | pairID), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  exp3_model_v3 <- brm(
    n_touching | trials(n) ~ hive + (1 | pairID), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = c(set_prior("normal(0, 3)", class = "b")),
    family = "binomial",  save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  posterior_model_probabilities <- tibble(
    Model = c("treatment * hive + observation_time_minutes",
              "treatment + hive + observation_time_minutes",
              "hive + observation_time_minutes"),
    post_prob = as.numeric(post_prob(exp3_model_v1,
                                     exp3_model_v2,
                                     exp3_model_v3))) %>%
    arrange(-post_prob)
  
  saveRDS(exp3_model_v2, "output/exp3_model.rds") # save the top model, treatment + hive
  saveRDS(posterior_model_probabilities, "output/exp3_post_prob.rds")
}
exp3_model <- readRDS("output/exp3_model.rds")
model_probabilities <- readRDS("output/exp3_post_prob.rds")

Posterior model probabilites

model_probabilities %>% 
  kable(digits = 3) %>% kable_styling(full_width = FALSE)
Model post_prob
hive + observation_time_minutes 0.720
treatment + hive + observation_time_minutes 0.278
treatment * hive + observation_time_minutes 0.001

Fixed effects from the top model

Raw output of the treatment + hive model

summary(exp3_model)
 Family: binomial 
  Links: mu = logit 
Formula: n_touching | trials(n) ~ treatment + hive + (1 | tube) 
   Data: expt3_counts %>% mutate(n = n_touching + n_not_tou (Number of observations: 439) 
Samples: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
         total post-warmup samples = 40000

Group-Level Effects: 
~tube (Number of levels: 439) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     2.02      0.08     1.87     2.19 1.00     3481     6133

Population-Level Effects: 
             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept        1.68      0.14     1.40     1.96 1.00     1542     2621
treatmentLPS    -0.37      0.20    -0.76     0.02 1.00     1508     3329
hive1           -0.20      0.17    -0.54     0.14 1.01     1423     2879
hive2            0.14      0.16    -0.16     0.46 1.00     1302     2268
hive3           -0.23      0.18    -0.58     0.12 1.00     1245     2518

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Formatted brms output for Table S5

The code chunk below wrangles the raw output of the summary() function for brms models into a more readable table of results, and also adds ‘Bayesian p-values’ (i.e. the posterior probability that the true effect size has the same sign as the reported effect).


Table S5: Table summarising the posterior estimates of each fixed effect in the best-fitting model of Experiment 3 that contained the treatment effect. This was a binomial model where the response variable was 0 for observations in which bees were not in close contact, and 1 when they were. ‘Treatment’ is a fixed factor with two levels, and the effect of LPS shown here is expressed relative to the ‘Ringers’ treatment. ‘Hive’ was a fixed factor with four levels; unlike for treatment, we modelled hive using deviation coding, such that the intercept term represents the mean across all hives (in the Ringers treatment), and the three hive terms represent the deviation from this mean for three of the four hives. The model also included a random effect ‘pair ID’ (XXXXX), which grouped repeated observations made on each pair of bees, preventing pseudoreplication. The \(p\) column gives the posterior probability that the true effect size is opposite in sign to what is reported in the Estimate column, similarly to a p-value.

tableS5 <- get_fixed_effects_with_p_values(exp3_model) %>% 
  mutate(mu = map_chr(str_extract_all(Parameter, "mu[:digit:]"), ~ .x[1]),
         Parameter = str_remove_all(Parameter, "mu[:digit:]_"),
         Parameter = str_replace_all(Parameter, "treatment", "Treatment: "),
         Parameter = str_replace_all(Parameter, "observation_time_minutes", "Observation duration (minutes)")) %>%
  arrange(mu) %>%
  select(-mu, -Rhat, -Bulk_ESS, -Tail_ESS) 

names(tableS5)[3:5] <- c("Est. Error", "Lower 95% CI", "Upper 95% CI")

saveRDS(tableS5, file = "figures/tableS5.rds")

tableS5 %>%
  kable(digits = 3) %>% 
  kable_styling(full_width = FALSE) 
Parameter Estimate Est. Error Lower 95% CI Upper 95% CI PP
Intercept 1.678 0.141 1.401 1.960 0.000 ***
Treatment: LPS -0.369 0.199 -0.763 0.022 0.033 *
hive1 -0.198 0.175 -0.539 0.137 0.130
hive2 0.145 0.158 -0.157 0.462 0.180
hive3 -0.227 0.179 -0.582 0.121 0.102

Plotting estimates from the model

new <- expt3_counts %>% 
  select(treatment) %>% distinct() %>% 
  mutate(n = 100, key = paste("V", 1:n(), sep = ""),
         hive = NA) 
plotting_data <- as.data.frame(fitted(exp3_model, 
                                      newdata=new, re_formula = NA, summary = FALSE))
names(plotting_data) <- c("LPS", "Ringers")
plotting_data <- plotting_data %>% gather(treatment, percent_time_in_contact)

panel_c_colour <- "#CC79A7"

dot_plot <- plotting_data %>%
  mutate(treatment = factor(treatment, c("Ringers", "LPS"))) %>%
  ggplot(aes(percent_time_in_contact, treatment)) + 
  stat_dotsh(quantiles = 100, fill = "grey40", colour = "grey40") + 
  stat_pointintervalh(
    mapping = aes(colour = treatment, fill = treatment),
    .width = c(0.5, 0.95), 
    position = position_nudge(y = -0.07),
    point_colour = "grey26", pch = 21, stroke = 0.4) + 
  xlab("Mean % time in close contact") + ylab("Treatment") + 
  scale_colour_brewer(palette = "Pastel1", 
                      direction = -1, name = "Treatment") +
  scale_fill_brewer(palette = "Pastel1", 
                      direction = -1, name = "Treatment") +
  theme_bw() + 
  coord_cartesian(ylim=c(1.4, 2.4)) + 
  theme(
    text = element_text(family = nice_font),
    strip.background = element_rect(fill = "#eff0f1"),
    panel.grid.major.y = element_blank(),
    legend.position = "none"
  ) 
  
# positive effect = odds of this outcome are higher for trt2 than trt1 (put control as trt1)
get_log_odds <- function(trt1, trt2){ 
  log((trt2 / (1 - trt2) / (trt1 / (1 - trt1))))
}

LOR <- plotting_data %>%
  mutate(posterior_sample = rep(1:(n()/2), 2)) %>%
  spread(treatment, percent_time_in_contact) %>%
  mutate(LOR = get_log_odds(Ringers/100, LPS/100)) %>%
  select(LOR)

LOR_plot <- LOR %>%
  ggplot(aes(LOR, y =1)) + 
  geom_vline(xintercept = 0, linetype = 2) +
  stat_dotsh(quantiles = 100, fill = "grey40", colour = "grey40") + 
  stat_pointintervalh(
    colour = panel_c_colour, fill = panel_c_colour,
    .width = c(0.5, 0.95), 
    position = position_nudge(y = -0.1),
    point_colour = "grey26", pch = 21, stroke = 0.4) + 
  coord_cartesian(ylim=c(0.86, 2)) + 
  xlab("Effect of LPS on mean\n% time in close contact (LOR)") + 
  ylab("Posterior density") + 
  theme_bw() +
  theme(
    text = element_text(family = nice_font),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank(),
    panel.grid.major.y = element_blank(),
    panel.grid.minor.y = element_blank(),
    legend.position = "none"
  ) 
 
p <- cowplot::plot_grid(raw_histogram, 
                        dot_plot, LOR_plot, labels = c("A", "B", "C"),
                        nrow = 1, align = 'h', axis = 'l')
ggsave(plot = p, filename = "figures/fig3.pdf", height = 3.2, width = 8.6)
p

Version Author Date
f188968 lukeholman 2020-05-02

Figure 3: Panel A shows the frequency distribution of the % time in close contact, for pairs of bees from the LPS treatment and the Ringers control. Panel B shows the posterior estimates of the mean % time spent in close contact; the details of the quantile dot plot and error bars are the same as described for Figure 1. Panel C shows the effect size (LOR; log odds ratio) associated with the difference in means in Panel B.

Hypothesis testing and effect sizes

get_log_odds <- function(trt1, trt2){ 
  log((trt2 / (1 - trt2) / (trt1 / (1 - trt1))))
}

my_summary <- function(df) {
  
  diff <- (df %>% pull(Ringers)) - (df %>% pull(LPS))
  LOR <- get_log_odds((df %>% pull(Ringers))/100, 
                      (df %>% pull(LPS))/100)
  p <- 1 - (diff %>% bayestestR::p_direction() %>% as.numeric())
  diff <- diff %>% posterior_summary() %>% as_tibble()
  LOR <- LOR %>% posterior_summary() %>% as_tibble()
  output <- rbind(diff, LOR) %>% 
    mutate(p=p, 
           Metric = c("Absolute difference in % time in close contact", 
                      "Log odds ratio")) %>% 
      select(Metric, everything()) %>%
    mutate(p = format(round(p, 4), nsmall = 4))
  output$p[1] <- " "
  output
}

plotting_data %>%
  as_tibble() %>%
  mutate(sample = rep(1:(n() / 2), 2)) %>%
  spread(treatment, percent_time_in_contact) %>%
  mutate(difference = LPS - Ringers) %>%
  my_summary() %>%
  mutate(` ` = ifelse(p < 0.05, "\\*", ""),
         ` ` = replace(` `, p < 0.01, "**"),
         ` ` = replace(` `, p < 0.001, "***"),
         ` ` = replace(` `, p == " ", "")) %>%
  kable(digits = 3) %>% kable_styling() 
Metric Estimate Est.Error Q2.5 Q97.5 p
Absolute difference in % time in close contact 5.538 3.006 -0.330 11.495
Log odds ratio -0.369 0.199 -0.763 0.022 0.0328 *

Table S6: Pairs in which one bee had received LPS were observed in close contact less frequently than pairs in which one bee had received Ringers solution.


sessionInfo()
R version 3.6.3 (2020-02-29)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_AU.UTF-8/en_AU.UTF-8/en_AU.UTF-8/C/en_AU.UTF-8/en_AU.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] scales_1.1.0     tidybayes_2.0.1  cowplot_1.0.0    bayestestR_0.5.1 kableExtra_1.1.0 gridExtra_2.3   
 [7] forcats_0.5.0    stringr_1.4.0    dplyr_0.8.5      purrr_0.3.3      readr_1.3.1      tidyr_1.0.2     
[13] tibble_3.0.0     ggplot2_3.3.0    tidyverse_1.3.0  bayesplot_1.7.1  brms_2.12.0      Rcpp_1.0.4.6    
[19] showtext_0.7-1   showtextdb_2.0   sysfonts_0.8     workflowr_1.6.1 

loaded via a namespace (and not attached):
  [1] colorspace_1.4-1     ellipsis_0.3.0       ggridges_0.5.2       rsconnect_0.8.16     rprojroot_1.3-2     
  [6] markdown_1.1         base64enc_0.1-3      fs_1.4.1             rstudioapi_0.11      farver_2.0.3        
 [11] rstan_2.19.3         svUnit_0.7-12        DT_0.13              fansi_0.4.1          mvtnorm_1.1-0       
 [16] lubridate_1.7.8      xml2_1.3.1           bridgesampling_1.0-0 knitr_1.28           shinythemes_1.1.2   
 [21] jsonlite_1.6.1       broom_0.5.4          dbplyr_1.4.2         shiny_1.4.0.2        compiler_3.6.3      
 [26] httr_1.4.1           backports_1.1.6      assertthat_0.2.1     Matrix_1.2-18        fastmap_1.0.1       
 [31] cli_2.0.2            later_1.0.0          htmltools_0.4.0.9003 prettyunits_1.1.1    tools_3.6.3         
 [36] igraph_1.2.5         coda_0.19-3          gtable_0.3.0         glue_1.4.0           reshape2_1.4.4      
 [41] cellranger_1.1.0     vctrs_0.2.4          nlme_3.1-147         crosstalk_1.1.0.1    insight_0.8.1       
 [46] xfun_0.13            ps_1.3.0             rvest_0.3.5          mime_0.9             miniUI_0.1.1.1      
 [51] lifecycle_0.2.0      gtools_3.8.2         zoo_1.8-7            colourpicker_1.0     hms_0.5.3           
 [56] promises_1.1.0       Brobdingnag_1.2-6    parallel_3.6.3       inline_0.3.15        RColorBrewer_1.1-2  
 [61] shinystan_2.5.0      curl_4.3             yaml_2.2.1           loo_2.2.0            StanHeaders_2.19.2  
 [66] stringi_1.4.6        highr_0.8            dygraphs_1.1.1.6     pkgbuild_1.0.6       rlang_0.4.5         
 [71] pkgconfig_2.0.3      matrixStats_0.56.0   evaluate_0.14        lattice_0.20-41      labeling_0.3        
 [76] rstantools_2.0.0     htmlwidgets_1.5.1    processx_3.4.2       tidyselect_1.0.0     plyr_1.8.6          
 [81] magrittr_1.5         R6_2.4.1             generics_0.0.2       DBI_1.1.0            pillar_1.4.3        
 [86] haven_2.2.0          whisker_0.4          withr_2.1.2          xts_0.12-0           abind_1.4-5         
 [91] modelr_0.1.5         crayon_1.3.4         arrayhelpers_1.1-0   rmarkdown_2.1.3      grid_3.6.3          
 [96] readxl_1.3.1         callr_3.4.3          git2r_0.26.1         threejs_0.3.3        reprex_0.3.0        
[101] digest_0.6.25        webshot_0.5.2        xtable_1.8-4         httpuv_1.5.2         stats4_3.6.3        
[106] munsell_0.5.0        viridisLite_0.3.0    shinyjs_1.1