Metabolic rates
Martin Garlovsky
11/23/2020
Last updated: 2020-11-24
Checks: 5 1
Knit directory: ~/Dropbox/psephysiology/
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Load packages
library(tidyverse)
library(GGally)
library(gridExtra)
library(ggridges)
library(nlme)
library(brms)
library(tidybayes)
library(kableExtra)
library(knitrhooks) # install with devtools::install_github("nathaneastwood/knitrhooks")
output_max_height() # a knitrhook option
options(stringsAsFactors = FALSE)Load metabolite composition data
dat1 <- read.csv('data/3.metabolite_data.csv')
# subset data, keep only raw variables and scale
metdat <- dat1 %>%
# keep only second timepoint (3d old)
filter(time == '2') %>%
# scale variables
mutate(fwt = as.numeric(scale(fwt_mg)),
dwt = as.numeric(scale(dwt_mg)),
Hex = as.numeric(scale(Hex_frac)),
Aqf = as.numeric(scale(Aq_frac)),
Pro = as.numeric(scale(Protein)),
Gly = as.numeric(scale(Glycogen)),
Chi = as.numeric(scale(Chitin))) %>%
# keep only raw measurements - calculate fractional data later
select(sex, treatment, LINE = line, fwt, dwt, Hex, Aqf, Pro, Gly, Chi) %>%
mutate(Wat = fwt - dwt)Subset data to keep only raw variables and then scale - will want to do this cleaning step prior to upload for real thing
metdat <- dat1 %>%
# keep only second timepoint (3d old)
filter(time == '2') %>%
# scale variables
mutate(fwt = as.numeric(scale(fwt_mg)),
dwt = as.numeric(scale(dwt_mg)),
Hex = as.numeric(scale(Hex_frac)),
Aqf = as.numeric(scale(Aq_frac)),
Pro = as.numeric(scale(Protein)),
Gly = as.numeric(scale(Glycogen)),
Chi = as.numeric(scale(Chitin))) %>%
# keep only raw measurements - calculate fractional data later
select(sex, treatment, LINE = line, -fwt, dwt, Aqf, Chi, Gly, Hex, Pro)This analysis set out to test whether sexual selection treatment had an effect on metabolite composition of flies. We measured dry fly weight dwt and five metabolites which together equal the dry weight; Hex (hexane fraction, lipids), Aqf (aqueous fraction, soluble carbohydrates), Pro (protein), Gly (glycogen), and Chi (chitin). We expect body weight to vary between the sexes and potentially between treatments. In turn, we expect body weight to affect our five response variables of interest. Larger flies will have more lipids, carbs, etc., and this may vary by sex and treatment both directly and indirectly.
DAG
DiagrammeR::grViz('digraph {
graph [layout = dot, rankdir = LR]
# define the global styles of the nodes. We can override these in box if we wish
node [shape = rectangle, style = filled, fillcolor = Linen]
"Metabolite\ncomposition" [shape = oval, fillcolor = Beige]
# edge definitions with the node IDs
"Mating system\ntreatment (M vs P)" -> {"Body mass"}
"Mating system\ntreatment (M vs P)" -> {"Metabolite\ncomposition"}
"Sex\n(Female vs Male)" -> {"Body mass"} -> {"Metabolite\ncomposition"}
"Sex\n(Female vs Male)" -> {"Metabolite\ncomposition"}
{"Metabolite\ncomposition"} -> "Lipids"
{"Metabolite\ncomposition"} -> "Carbohydrates"
{"Metabolite\ncomposition"} -> "Glycogen"
{"Metabolite\ncomposition"} -> "Protein"
{"Metabolite\ncomposition"} -> "Chitin"
}')Inspecting the raw data
metdat %>%
reshape2::melt(id.vars = c('sex', 'treatment', 'LINE', 'dwt')) %>%
ggplot(aes(x = dwt, y = value, colour = treatment)) +
geom_point() +
geom_smooth(method = 'lm', se = FALSE) +
scale_colour_brewer(palette = 'Set1', direction = -1, name = "") +
facet_grid(sex ~ variable) +
theme_bw() +
theme(legend.position = 'top') +
NULL
A pairs plot also goes here using Luke’s custom plot - need to check how to incorporate that function
R chunk for pairs plot
Fit the multivariate brms model
Fit brms SEM
Here I fit a model including body weight as a mediator variable. That is, body weight potentially varies between the sexes and between selection treatments, and body weight may also directly influence the five response variables. The model allows for fixed effects of selection and sex and their interaction with body weight. The three-way selection x sex x body weight interaction allows the effect of selection on the response variable to vary between the sexes, and with a different slope for body weight.
Priors
As with Luke’s analysis, set priors for all fixed effect parameters normal(0,1). Although Luke had sd = 3. Additionally set priors for random effects
# set priors
prior1 <- c(set_prior("normal(0,0.1)", class = "b", resp = 'Aqf'),
set_prior("normal(0,0.1)", class = "b", resp = 'Chi'),
set_prior("normal(0,0.1)", class = "b", resp = 'Gly'),
set_prior("normal(0,0.1)", class = "b", resp = 'Hex'),
set_prior("normal(0,0.1)", class = "b", resp = 'Pro'),
set_prior("normal(0,0.1)", class = "b", resp = 'dwt'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'Aqf'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'Chi'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'Gly'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'Hex'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'Pro'),
set_prior("cauchy(0,0.1)", class = "sd", resp = 'dwt'))brms_formula <-
bf(mvbind(Hex, Aqf, Pro, Gly, Chi) ~
sex * treatment * dwt + (1|p|LINE)) +
# body mass sub-model
bf(dwt ~ sex * treatment +
(1|p|LINE)) +
set_rescor(FALSE)
# brms_SEM <- brm(
# brms_formula,
# data = metdat,
# iter = 5000, chains = 4, cores = 4,
# prior = prior1,
# control = list(max_treedepth = 20,
# adapt_delta = 0.999)
# )
# load in the model instead of running
brms_SEM <- readRDS('output/brms_SEM.rds')grid.arrange(
pp_check(brms_SEM, resp = "Aqf") + ggtitle("Aqf") + theme(legend.position = "none"),
pp_check(brms_SEM, resp = "Chi") + ggtitle("Chi") + theme(legend.position = "none"),
pp_check(brms_SEM, resp = "Gly") + ggtitle("Gly") + theme(legend.position = "none"),
pp_check(brms_SEM, resp = "Hex") + ggtitle("Hex") + theme(legend.position = "none"),
pp_check(brms_SEM, resp = "Pro") + ggtitle("Pro") + theme(legend.position = "none"),
nrow = 1
)
Plot posteriors for response variables and body size separately.
# get posterior predictions
post_dat <- posterior_samples(brms_SEM) %>%
as_tibble() %>%
select(contains("b_"), -contains("Intercept")) %>%
mutate(draw = 1:n()) %>%
pivot_longer(-draw) %>%
mutate(key = str_remove_all(name, "b_"),
var = gsub("_.*", "", x = key),
eff = gsub(".*_", "", x = key))
post_dat %>%
filter(var != 'dwt') %>%
ggplot(aes(value, eff, fill = eff)) +
geom_vline(xintercept = 0, linetype = 2) +
stat_halfeye(alpha = .8) +
scale_fill_brewer(palette = "Spectral") +
ylab("Model parameter") +
xlab("Effect on Metabolite weight") +
facet_wrap(~ var, nrow = 1) +
theme_ridges() +
theme(legend.position = "none") +
NULL
post_dat %>%
filter(var == 'dwt') %>%
ggplot(aes(value, eff, fill = eff)) +
geom_vline(xintercept = 0, linetype = 2) +
stat_halfeye(alpha = .8) +
scale_fill_brewer(palette = "Spectral") +
ylab("Model parameter") +
xlab("Effect on Body weight") +
theme_ridges() +
theme(legend.position = "none") +
NULL
Summary of the results of the full model
data.frame(param = rownames(fixef(brms_SEM)),
fixef(brms_SEM)) %>%
mutate(var = gsub('_.*', '', x = param),
par = gsub('.*_', '', x = param),
var2 = gsub('dwt', 'zdwt', var),
star = if_else(sign(Q2.5) == sign(Q97.5), '*', '')) %>%
select(var2, par, Estimate, Est.Error, Q2.5, Q97.5, star) %>%
arrange(var2) %>%
select(Parameter = par, Estimate, Est.Error, Q2.5, Q97.5, star) %>%
mutate(Parameter = c(rep(c('Intercept', 'Male', 'Polandry', 'Body weight',
'Polandry x Male', 'Body weight x Male', 'Polyandry x Body weight',
'Polyandry x Male x Body weight'), 5),
'Intercept', 'Male', 'Polyandry', 'Polyandry x Male')) %>%
kable() %>%
kable_styling() %>%
kable_styling(full_width = FALSE) %>%
group_rows("Carbohydrates", 1, 8) %>%
group_rows("Chitin", 9, 16) %>%
group_rows("Glycogen", 17, 24) %>%
group_rows("Lipids", 25, 32) %>%
group_rows("Protein", 33, 40) %>%
group_rows("Body weight", 41, 44)| Parameter | Estimate | Est.Error | Q2.5 | Q97.5 | star |
|---|---|---|---|---|---|
| Carbohydrates | |||||
| Intercept | 0.1714983 | 0.1349144 | -0.0945009 | 0.4364838 | |
| Male | -0.1518639 | 0.0928750 | -0.3336862 | 0.0285726 | |
| Polandry | -0.0272399 | 0.0881125 | -0.1971564 | 0.1450494 | |
| Body weight | 0.3386260 | 0.0835475 | 0.1729942 | 0.5025976 |
|
| Polandry x Male | -0.0806061 | 0.0922942 | -0.2610999 | 0.0983601 | |
| Body weight x Male | 0.1366700 | 0.0931816 | -0.0449952 | 0.3222993 | |
| Polyandry x Body weight | 0.1550002 | 0.0834759 | -0.0086002 | 0.3222961 | |
| Polyandry x Male x Body weight | 0.0630317 | 0.0965411 | -0.1241364 | 0.2519342 | |
| Chitin | |||||
| Intercept | 0.0452885 | 0.2319819 | -0.4208547 | 0.4873574 | |
| Male | -0.0188831 | 0.0951880 | -0.2024412 | 0.1666103 | |
| Polandry | -0.0196953 | 0.0936917 | -0.2031056 | 0.1654647 | |
| Body weight | 0.0892243 | 0.0856931 | -0.0797229 | 0.2561783 | |
| Polandry x Male | -0.0265415 | 0.0966752 | -0.2175734 | 0.1657149 | |
| Body weight x Male | 0.0425495 | 0.0956188 | -0.1411421 | 0.2309482 | |
| Polyandry x Body weight | 0.0683646 | 0.0909855 | -0.1118619 | 0.2474581 | |
| Polyandry x Male x Body weight | 0.0438118 | 0.0951648 | -0.1416162 | 0.2292286 | |
| Glycogen | |||||
| Intercept | 0.0287643 | 0.1619038 | -0.2891110 | 0.3460149 | |
| Male | -0.0648606 | 0.0964365 | -0.2550203 | 0.1223700 | |
| Polandry | 0.0502960 | 0.0936436 | -0.1346089 | 0.2329895 | |
| Body weight | 0.1927455 | 0.0887444 | 0.0138473 | 0.3643072 |
|
| Polandry x Male | 0.0032513 | 0.0964376 | -0.1838628 | 0.1923192 | |
| Body weight x Male | 0.0655607 | 0.0961830 | -0.1219661 | 0.2495521 | |
| Polyandry x Body weight | 0.0807752 | 0.0901056 | -0.0932273 | 0.2581921 | |
| Polyandry x Male x Body weight | -0.0019626 | 0.0953672 | -0.1917484 | 0.1835361 | |
| Lipids | |||||
| Intercept | 0.0398499 | 0.1345951 | -0.2243927 | 0.3050826 | |
| Male | -0.1226856 | 0.0959817 | -0.3129218 | 0.0610563 | |
| Polandry | 0.1258373 | 0.0885150 | -0.0480276 | 0.2975061 | |
| Body weight | 0.3683435 | 0.0831640 | 0.2036315 | 0.5308176 |
|
| Polandry x Male | -0.0063785 | 0.0941639 | -0.1901252 | 0.1769372 | |
| Body weight x Male | 0.1263877 | 0.0937854 | -0.0614751 | 0.3098339 | |
| Polyandry x Body weight | 0.2130393 | 0.0848081 | 0.0454402 | 0.3769011 |
|
| Polyandry x Male x Body weight | 0.0083977 | 0.0950130 | -0.1769160 | 0.1961643 | |
| Protein | |||||
| Intercept | 0.1571959 | 0.1443347 | -0.1207632 | 0.4293221 | |
| Male | -0.1603434 | 0.0948598 | -0.3451387 | 0.0277937 | |
| Polandry | 0.0127451 | 0.0900325 | -0.1616061 | 0.1901971 | |
| Body weight | 0.3277234 | 0.0825826 | 0.1615875 | 0.4885108 |
|
| Polandry x Male | -0.0312713 | 0.0931886 | -0.2106957 | 0.1484134 | |
| Body weight x Male | 0.1746670 | 0.0969503 | -0.0177338 | 0.3660244 | |
| Polyandry x Body weight | 0.1021757 | 0.0852404 | -0.0629964 | 0.2706162 | |
| Polyandry x Male x Body weight | 0.0317577 | 0.0956811 | -0.1521720 | 0.2197227 | |
| Body weight | |||||
| Intercept | 0.1167671 | 0.1618532 | -0.2098954 | 0.4333520 | |
| Male | -0.2390697 | 0.1072820 | -0.4537327 | -0.0313626 |
|
| Polyandry | 0.0572130 | 0.0936381 | -0.1275896 | 0.2408248 | |
| Polyandry x Male | -0.1028201 | 0.0966760 | -0.2859933 | 0.0840322 | |
Body weight has a positive effect on Aqf, Gly, Hex, and Pro. Larger flies contain more of these metabolites. There is also evidence of a treatment x body weight interaction for Hex. Hex increases with body weight moreso in polyandrous flies (steeper slope). There is a sex effect on body weight (as expected). Males weigh less than females.
Extract posterior estimates of the means and plotting…
# fitbrms_SEM <- metdat %>%
# modelr::data_grid(treatment, sex, LINE, dwt) %>%
# add_fitted_draws(brms_SEM) %>%
# sample_frac(size = .5)
fitbrms_SEM <- readRDS('output/fitbrms_SEM.rds')
fitbrms_SEM %>%
filter(.category != 'dwt') %>%
group_by(treatment, sex, dwt, .category) %>%
summarise(mn = mean(.value),
lwr = qnorm(0.975)*sd(.value)/sqrt(n()),
upr = qnorm(0.975)*sd(.value)/sqrt(n())) %>%
ggplot(aes(x = dwt, y = mn, colour = treatment)) +
geom_ribbon(aes(ymin = mn - lwr, ymax = mn + upr, fill = treatment)) +
scale_fill_brewer(palette = 'Set1', direction = -1, name = "") +
scale_colour_brewer(palette = 'Set1', direction = -1, name = "") +
facet_grid(sex ~ .category) +
theme_bw() +
theme(legend.position = 'top') +
NULL
Hypothesis testing
Using the hypothesis function I loop through each response variable to test difference from intercept (monogamy females. This is essentially the same as the summary table from the fit.
vars <- c("Aqf", "Chi", "Gly", "Hex", "Pro")
tests <- c('_dwt', '_sexm', '_sexm:dwt', '_sexm:treatmentP', '_sexm:treatmentP:dwt',
'_treatmentP', '_treatmentP:dwt')
hypSEM <- data.frame(expand_grid(vars, tests) %>%
mutate(est = NA,
err = NA,
lwr = NA,
upr = NA,
star = NA) %>%
rbind(data.frame(vars = rep('dwt', 3),
tests = c('_sexm', '_treatmentP', '_sexm:treatmentP'),
est = NA,
err = NA,
lwr = NA,
upr = NA,
star = NA)))
for(i in 1:nrow(hypSEM)) {
result = hypothesis(brms_SEM, paste0(hypSEM[i, 1], hypSEM[i, 2], ' = 0'))$hypothesis
hypSEM[i, 3] = round(result$Estimate, 3)
hypSEM[i, 4] = round(result$Est.Error, 3)
hypSEM[i, 5] = round(result$CI.Lower, 3)
hypSEM[i, 6] = round(result$CI.Upper, 3)
hypSEM[i, 7] = result$Star
}
hypSEM %>%
select(Parameter = tests, Estimate = est, `Est. error` = err, `CI lower` = lwr, `CI upper` = upr, star) %>%
mutate(Parameter = c(rep(c('Body weight', 'Male', 'Male x Body weight',
'Male x Polyandry', 'Body weight x Polyandry x Male',
'Polandry', 'Body weight x Polyandry'), 5),
'Male', 'Polyandry', 'Male x Polyandry')) %>%
kable() %>%
kable_styling(full_width = FALSE) %>%
group_rows("Carbohydrates", 1, 7) %>%
group_rows("Chitin", 8, 14) %>%
group_rows("Glycogen", 15, 21) %>%
group_rows("Lipids", 22, 28) %>%
group_rows("Protein", 29, 35) %>%
group_rows("Body weight", 36, 38)| Parameter | Estimate | Est. error | CI lower | CI upper | star |
|---|---|---|---|---|---|
| Carbohydrates | |||||
| Body weight | 0.339 | 0.084 | 0.173 | 0.503 |
|
| Male | -0.152 | 0.093 | -0.334 | 0.029 | |
| Male x Body weight | 0.137 | 0.093 | -0.045 | 0.322 | |
| Male x Polyandry | -0.081 | 0.092 | -0.261 | 0.098 | |
| Body weight x Polyandry x Male | 0.063 | 0.097 | -0.124 | 0.252 | |
| Polandry | -0.027 | 0.088 | -0.197 | 0.145 | |
| Body weight x Polyandry | 0.155 | 0.083 | -0.009 | 0.322 | |
| Chitin | |||||
| Body weight | 0.089 | 0.086 | -0.080 | 0.256 | |
| Male | -0.019 | 0.095 | -0.202 | 0.167 | |
| Male x Body weight | 0.043 | 0.096 | -0.141 | 0.231 | |
| Male x Polyandry | -0.027 | 0.097 | -0.218 | 0.166 | |
| Body weight x Polyandry x Male | 0.044 | 0.095 | -0.142 | 0.229 | |
| Polandry | -0.020 | 0.094 | -0.203 | 0.165 | |
| Body weight x Polyandry | 0.068 | 0.091 | -0.112 | 0.247 | |
| Glycogen | |||||
| Body weight | 0.193 | 0.089 | 0.014 | 0.364 |
|
| Male | -0.065 | 0.096 | -0.255 | 0.122 | |
| Male x Body weight | 0.066 | 0.096 | -0.122 | 0.250 | |
| Male x Polyandry | 0.003 | 0.096 | -0.184 | 0.192 | |
| Body weight x Polyandry x Male | -0.002 | 0.095 | -0.192 | 0.184 | |
| Polandry | 0.050 | 0.094 | -0.135 | 0.233 | |
| Body weight x Polyandry | 0.081 | 0.090 | -0.093 | 0.258 | |
| Lipids | |||||
| Body weight | 0.368 | 0.083 | 0.204 | 0.531 |
|
| Male | -0.123 | 0.096 | -0.313 | 0.061 | |
| Male x Body weight | 0.126 | 0.094 | -0.061 | 0.310 | |
| Male x Polyandry | -0.006 | 0.094 | -0.190 | 0.177 | |
| Body weight x Polyandry x Male | 0.008 | 0.095 | -0.177 | 0.196 | |
| Polandry | 0.126 | 0.089 | -0.048 | 0.298 | |
| Body weight x Polyandry | 0.213 | 0.085 | 0.045 | 0.377 |
|
| Protein | |||||
| Body weight | 0.328 | 0.083 | 0.162 | 0.489 |
|
| Male | -0.160 | 0.095 | -0.345 | 0.028 | |
| Male x Body weight | 0.175 | 0.097 | -0.018 | 0.366 | |
| Male x Polyandry | -0.031 | 0.093 | -0.211 | 0.148 | |
| Body weight x Polyandry x Male | 0.032 | 0.096 | -0.152 | 0.220 | |
| Polandry | 0.013 | 0.090 | -0.162 | 0.190 | |
| Body weight x Polyandry | 0.102 | 0.085 | -0.063 | 0.271 | |
| Body weight | |||||
| Male | -0.239 | 0.107 | -0.454 | -0.031 |
|
| Polyandry | 0.057 | 0.094 | -0.128 | 0.241 | |
| Male x Polyandry | -0.103 | 0.097 | -0.286 | 0.084 | |
sessionInfo()R version 4.0.3 (2020-10-10) Platform: x86_64-apple-darwin17.0 (64-bit) Running under: macOS Mojave 10.14.6 Matrix products: default BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib locale: [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] knitrhooks_0.0.4 knitr_1.30 kableExtra_1.3.1 tidybayes_2.3.1 [5] brms_2.14.4 Rcpp_1.0.5 nlme_3.1-149 ggridges_0.5.2 [9] gridExtra_2.3 GGally_2.0.0 forcats_0.5.0 stringr_1.4.0 [13] dplyr_1.0.2 purrr_0.3.4 readr_1.4.0 tidyr_1.1.2 [17] tibble_3.0.4 ggplot2_3.3.2 tidyverse_1.3.0 loaded via a namespace (and not attached): [1] readxl_1.3.1 backports_1.1.10 workflowr_1.6.2 [4] plyr_1.8.6 igraph_1.2.6 splines_4.0.3 [7] svUnit_1.0.3 crosstalk_1.1.0.1 rstantools_2.1.1 [10] inline_0.3.16 digest_0.6.25 htmltools_0.5.0 [13] rsconnect_0.8.16 fansi_0.4.1 magrittr_2.0.1 [16] modelr_0.1.8 RcppParallel_5.0.2 matrixStats_0.57.0 [19] xts_0.12.1 prettyunits_1.1.1 colorspace_1.4-1 [22] blob_1.2.1 rvest_0.3.6 ggdist_2.3.0 [25] haven_2.3.1 xfun_0.19 callr_3.5.1 [28] crayon_1.3.4 jsonlite_1.7.1 lme4_1.1-23 [31] zoo_1.8-8 glue_1.4.2 gtable_0.3.0 [34] webshot_0.5.2 V8_3.4.0 distributional_0.2.1 [37] pkgbuild_1.1.0 rstan_2.21.2 abind_1.4-5 [40] scales_1.1.1 mvtnorm_1.1-1 DBI_1.1.0 [43] miniUI_0.1.1.1 viridisLite_0.3.0 xtable_1.8-4 [46] stats4_4.0.3 StanHeaders_2.21.0-6 DT_0.16 [49] htmlwidgets_1.5.2 httr_1.4.2 DiagrammeR_1.0.6.1 [52] threejs_0.3.3 arrayhelpers_1.1-0 RColorBrewer_1.1-2 [55] ellipsis_0.3.1 pkgconfig_2.0.3 reshape_0.8.8 [58] loo_2.3.1 farver_2.0.3 dbplyr_1.4.4 [61] labeling_0.3 tidyselect_1.1.0 rlang_0.4.8 [64] reshape2_1.4.4 later_1.1.0.1 visNetwork_2.0.9 [67] munsell_0.5.0 cellranger_1.1.0 tools_4.0.3 [70] cli_2.1.0 generics_0.0.2 broom_0.7.1 [73] evaluate_0.14 fastmap_1.0.1 yaml_2.2.1 [76] processx_3.4.4 fs_1.5.0 mime_0.9 [79] projpred_2.0.2 xml2_1.3.2 compiler_4.0.3 [82] bayesplot_1.7.2 shinythemes_1.1.2 rstudioapi_0.11 [85] gamm4_0.2-6 curl_4.3 reprex_0.3.0 [88] statmod_1.4.34 stringi_1.5.3 highr_0.8 [91] ps_1.4.0 Brobdingnag_1.2-6 lattice_0.20-41 [94] Matrix_1.2-18 nloptr_1.2.2.2 markdown_1.1 [97] shinyjs_2.0.0 vctrs_0.3.4 pillar_1.4.6 [100] lifecycle_0.2.0 bridgesampling_1.0-0 httpuv_1.5.4 [103] R6_2.4.1 promises_1.1.1 codetools_0.2-16 [106] boot_1.3-25 colourpicker_1.1.0 MASS_7.3-53 [109] gtools_3.8.2 assertthat_0.2.1 rprojroot_1.3-2 [112] withr_2.3.0 shinystan_2.5.0 mgcv_1.8-33 [115] parallel_4.0.3 hms_0.5.3 grid_4.0.3 [118] coda_0.19-4 minqa_1.2.4 rmarkdown_2.4 [121] git2r_0.27.1 shiny_1.5.0 lubridate_1.7.9 [124] base64enc_0.1-3 dygraphs_1.1.1.6