Analysis of Experiment 3
Last updated: 2020-04-21
Checks: 6 1
Knit directory: social_immunity/
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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)
source("code/helper_functions.R")
# set up nice font for figure
nice_font <- "PT Serif"
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"))
expt3_counts <- experiment3 %>%
group_by(treatment, tube, 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(hive = C(factor(hive), sum)) # sum coding for hiveInspect the raw data
Sample sizes by treatment
expt3_counts %>%
group_by(treatment) %>%
summarise(n = n()) %>%
kable() %>% kable_styling(full_width = FALSE)| treatment | n |
|---|---|
| LPS | 219 |
| Ringers | 220 |
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 | LPS | 50 |
| Arts | Ringers | 50 |
| Garden | LPS | 70 |
| Garden | Ringers | 70 |
| Skylab | LPS | 49 |
| Skylab | Ringers | 50 |
| Zoology | LPS | 50 |
| Zoology | Ringers | 50 |
Inspect the results
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 | LPS | 72.547 | 0.033 | 50 |
| Arts | Ringers | 69.509 | 0.036 | 50 |
| Garden | LPS | 68.895 | 0.037 | 70 |
| Garden | Ringers | 76.752 | 0.033 | 70 |
| Skylab | LPS | 65.653 | 0.034 | 49 |
| Skylab | Ringers | 70.509 | 0.040 | 50 |
| Zoology | LPS | 73.019 | 0.037 | 50 |
| Zoology | Ringers | 84.075 | 0.021 | 50 |
Plotted as a density histogram
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.
raw_histogram <- expt3_counts %>%
filter(treatment == "Ringers") %>%
ggplot(aes(100 * percent,
fill = treatment)) +
geom_histogram(data = expt3_counts %>%
filter(treatment == "LPS"),
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(0.27, 0.8),
text = element_text(family = nice_font))
raw_histogram
Binomial model of time spent in contact
Run the models
Fit a binomial model, where the response is either a 0 (if bees were not in contact) or 1 (if they were). To assess the effects of our predictor variables, we compare 5 models with different fixed factors, ranking them by posterior model probability.
# new verison....
if(!file.exists("output/exp3_model.rds")){
exp3_model_v1 <- brm(
n_touching | trials(n) ~ treatment * hive + (1 | tube),
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 = 10000, seed = 1)
exp3_model_v2 <- brm(
n_touching | trials(n) ~ treatment + hive + (1 | tube),
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 = 10000, seed = 1)
exp3_model_v3 <- brm(
n_touching | trials(n) ~ hive + (1 | tube),
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 = 10000, 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 | 0.794 |
| treatment + hive + observation_time_minutes | 0.205 |
| treatment * hive + observation_time_minutes | 0.001 |
Fixed effects from the top non-null model
get_fixed_effects_with_p_values(exp3_model) %>%
kable(digits = 3) %>% kable_styling()| Parameter | Estimate | Est.Error | lower_95_CI | upper_95_CI | Rhat | Bulk_ESS | Tail_ESS | p | |
|---|---|---|---|---|---|---|---|---|---|
| Intercept | 1.304 | 0.139 | 1.030 | 1.579 | 1.009 | 644 | 1105 | 0.000 | *** |
| treatmentRingers | 0.371 | 0.194 | -0.023 | 0.750 | 1.009 | 644 | 1245 | 0.031 | * |
| hive1 | -0.194 | 0.177 | -0.537 | 0.156 | 1.005 | 457 | 706 | 0.131 | |
| hive2 | 0.146 | 0.164 | -0.176 | 0.477 | 1.016 | 563 | 1057 | 0.188 | |
| hive3 | -0.223 | 0.177 | -0.567 | 0.131 | 1.012 | 432 | 981 | 0.106 |
movement_files <- c("data/data_collection_sheets/hiveA_movement.csv",
"data/data_collection_sheets/hiveB_movement.csv",
"data/data_collection_sheets/hiveC_movement.csv",
"data/data_collection_sheets/hiveD_movement.csv")
movement <- map(1:4, ~ read_csv(movement_files[.x]) %>%
mutate(hive = c("A", "B", "C", "D")[.x]) %>%
gather(video, movement, -hive, -tube)) %>%
bind_rows() %>%
mutate(treatment = ifelse(substr(tube, 1, 1) %in% c("A", "B"), "AB", "CD")) %>%
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")) %>%
split(.$hive) %>%
map(~ .x %>% arrange(video) %>%
mutate(video = as.numeric(factor(video, unique(video))))) %>%
bind_rows() %>%
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"))
movement %>%
mutate(movement = factor(movement)) %>%
group_by(movement, treatment) %>%
summarise(n=n()) %>%
ggplot(aes(movement, n, fill = treatment)) +
geom_bar(stat = "identity", colour = "grey20", position = "dodge") +
scale_fill_brewer(palette="Pastel2", direction = 1)
library(brms)
mod <- brm(movement | cat(3) ~ treatment + (1 | tube),
data = movement %>% mutate(movement = movement + 1), family = cumulative())
marginal_effects(mod, categorical = T)
new <- expand.grid(hive = c("Arts", "Garden", "Skylab", "Zoology"),
treatment = c("Ringers", "LPS"))
data.frame(new, rbind(fitted(mod, newdata = new, re_formula = NA)[,,1],
fitted(mod, newdata = new, re_formula = NA)[,,2],
fitted(mod, newdata = new, re_formula = NA)[,,3])) %>%
mutate(movement = factor(rep(0:2, each = nrow(new)))) %>%
ggplot(aes(movement, Estimate, ymin = Q2.5, ymax=Q97.5, colour = treatment)) +
geom_errorbar(position = position_dodge(0.2), width = 0) +
geom_point(position = position_dodge(0.2)) +
facet_wrap(~ hive)Plotting estimates from the model
# new test...
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)
cols <- c("#34558b", "#4ec5a5", "#ffaf12")
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 = "orange", fill = "orange",
.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 % time\nin 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
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 | 5.567 | 2.937 | -0.336 | 11.403 | ||
| Log odds ratio | -0.371 | 0.194 | -0.750 | 0.023 | 0.0306 | * |
Table XX: 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] tidybayes_2.0.1 cowplot_1.0.0 bayestestR_0.5.1 kableExtra_1.1.0
[5] gridExtra_2.3 forcats_0.5.0 stringr_1.4.0 dplyr_0.8.5
[9] purrr_0.3.3 readr_1.3.1 tidyr_1.0.2 tibble_3.0.0
[13] ggplot2_3.3.0 tidyverse_1.3.0 bayesplot_1.7.1 brms_2.12.0
[17] Rcpp_1.0.3 showtext_0.7-1 showtextdb_2.0 sysfonts_0.8
[21] workflowr_1.6.0
loaded via a namespace (and not attached):
[1] colorspace_1.4-1 ellipsis_0.3.0 ggridges_0.5.2
[4] rsconnect_0.8.16 rprojroot_1.3-2 markdown_1.1
[7] base64enc_0.1-3 fs_1.3.1 rstudioapi_0.11
[10] farver_2.0.3 rstan_2.19.3 svUnit_0.7-12
[13] DT_0.13 fansi_0.4.1 mvtnorm_1.1-0
[16] lubridate_1.7.8 xml2_1.3.1 bridgesampling_1.0-0
[19] knitr_1.28 shinythemes_1.1.2 jsonlite_1.6.1
[22] broom_0.5.4 dbplyr_1.4.2 shiny_1.4.0
[25] compiler_3.6.3 httr_1.4.1 backports_1.1.6
[28] 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
[34] prettyunits_1.1.1 tools_3.6.3 igraph_1.2.5
[37] coda_0.19-3 gtable_0.3.0 glue_1.4.0
[40] reshape2_1.4.4 cellranger_1.1.0 vctrs_0.2.4
[43] 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
[49] mime_0.9 miniUI_0.1.1.1 lifecycle_0.2.0
[52] gtools_3.8.2 zoo_1.8-7 scales_1.1.0
[55] colourpicker_1.0 hms_0.5.3 promises_1.1.0
[58] Brobdingnag_1.2-6 parallel_3.6.3 inline_0.3.15
[61] RColorBrewer_1.1-2 shinystan_2.5.0 curl_4.3
[64] yaml_2.2.1 loo_2.2.0 StanHeaders_2.19.2
[67] stringi_1.4.6 highr_0.8 dygraphs_1.1.1.6
[70] pkgbuild_1.0.6 rlang_0.4.5 pkgconfig_2.0.3
[73] matrixStats_0.56.0 evaluate_0.14 lattice_0.20-41
[76] labeling_0.3 rstantools_2.0.0 htmlwidgets_1.5.1
[79] processx_3.4.2 tidyselect_1.0.0 plyr_1.8.6
[82] magrittr_1.5 R6_2.4.1 generics_0.0.2
[85] DBI_1.1.0 pillar_1.4.3 haven_2.2.0
[88] whisker_0.4 withr_2.1.2 xts_0.12-0
[91] abind_1.4-5 modelr_0.1.5 crayon_1.3.4
[94] arrayhelpers_1.1-0 rmarkdown_2.1 grid_3.6.3
[97] readxl_1.3.1 callr_3.4.3 git2r_0.26.1
[100] threejs_0.3.3 reprex_0.3.0 digest_0.6.25
[103] webshot_0.5.2 xtable_1.8-4 httpuv_1.5.2
[106] stats4_3.6.3 munsell_0.5.0 viridisLite_0.3.0
[109] shinyjs_1.1