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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(tidybayes)
library(cowplot)
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()

exp1_treatments <- c("Intact control", "Ringers", "Heat-treated LPS", "LPS")

durations <- read_csv("data/data_collection_sheets/experiment_durations.csv") %>%
  filter(experiment == 1) %>% select(-experiment)

outcome_tally <- read_csv(file = "data/clean_data/experiment_1_outcome_tally.csv") %>%
  mutate(outcome = replace(outcome, outcome == "Left of own volition", "Left voluntarily")) %>%
  mutate(outcome   = factor(outcome, levels = c("Stayed inside the hive", "Left voluntarily", "Forced out")),
         treatment = factor(treatment, levels = exp1_treatments)) 

# Re-formatted version of the same data, where each row is an individual bee. We need this format to run the brms model.
data_for_categorical_model <- outcome_tally %>%
  mutate(id = 1:n()) %>%
  split(.$id) %>%
  map(function(x){
    if(x$n[1] == 0) return(NULL)
    data.frame(
      treatment = x$treatment[1],
      hive = x$hive[1],
      colour = x$colour[1],
      outcome = rep(x$outcome[1], x$n))
  }) %>% do.call("rbind", .) %>% as_tibble() %>%
  arrange(hive, treatment) %>%
  mutate(outcome_numeric = as.numeric(outcome),
         hive = as.character(hive),
         treatment = factor(treatment, levels = exp1_treatments)) %>%
  left_join(durations, by = "hive") %>%
  mutate(hive = C(factor(hive), sum)) # use sum coding for the factor levels of "hive"

Inspect the raw data

Sample sizes by treatment

data_for_categorical_model %>%
  group_by(treatment) %>%
  summarise(n = n()) %>%
  kable() %>% kable_styling(full_width = FALSE)
treatment n
Intact control 321
Ringers 153
Heat-treated LPS 186
LPS 182

Sample sizes by treatment and hive

data_for_categorical_model %>%
  group_by(hive, treatment) %>%
  summarise(n = n()) %>%
  kable() %>% kable_styling(full_width = FALSE)
hive treatment n
Garden Intact control 77
Garden Ringers 41
Garden Heat-treated LPS 34
Garden LPS 37
SkyLab Intact control 105
SkyLab Heat-treated LPS 58
SkyLab LPS 43
Zoology Intact control 106
Zoology Ringers 80
Zoology Heat-treated LPS 67
Zoology LPS 67
Zoology_2 Intact control 33
Zoology_2 Ringers 32
Zoology_2 Heat-treated LPS 27
Zoology_2 LPS 35

Inspect the results

outcome_tally %>%
  select(-colour) %>% 
  kable(digits = 3) %>% kable_styling(full_width = FALSE) %>%
  scroll_box(height = "380px")
hive treatment outcome n
Garden Heat-treated LPS Stayed inside the hive 34
Garden Heat-treated LPS Left voluntarily 0
Garden Heat-treated LPS Forced out 0
Garden Intact control Stayed inside the hive 75
Garden Intact control Left voluntarily 0
Garden Intact control Forced out 2
Garden LPS Stayed inside the hive 37
Garden LPS Left voluntarily 0
Garden LPS Forced out 0
Garden Ringers Stayed inside the hive 41
Garden Ringers Left voluntarily 0
Garden Ringers Forced out 0
SkyLab Heat-treated LPS Stayed inside the hive 47
SkyLab Heat-treated LPS Left voluntarily 6
SkyLab Heat-treated LPS Forced out 5
SkyLab Intact control Stayed inside the hive 102
SkyLab Intact control Left voluntarily 3
SkyLab Intact control Forced out 0
SkyLab LPS Stayed inside the hive 35
SkyLab LPS Left voluntarily 6
SkyLab LPS Forced out 2
Zoology Heat-treated LPS Stayed inside the hive 59
Zoology Heat-treated LPS Left voluntarily 1
Zoology Heat-treated LPS Forced out 7
Zoology Intact control Stayed inside the hive 105
Zoology Intact control Left voluntarily 0
Zoology Intact control Forced out 1
Zoology LPS Stayed inside the hive 60
Zoology LPS Left voluntarily 2
Zoology LPS Forced out 5
Zoology Ringers Stayed inside the hive 74
Zoology Ringers Left voluntarily 1
Zoology Ringers Forced out 5
Zoology_2 Heat-treated LPS Stayed inside the hive 16
Zoology_2 Heat-treated LPS Left voluntarily 1
Zoology_2 Heat-treated LPS Forced out 10
Zoology_2 Intact control Stayed inside the hive 24
Zoology_2 Intact control Left voluntarily 1
Zoology_2 Intact control Forced out 8
Zoology_2 LPS Stayed inside the hive 21
Zoology_2 LPS Left voluntarily 2
Zoology_2 LPS Forced out 12
Zoology_2 Ringers Stayed inside the hive 23
Zoology_2 Ringers Left voluntarily 1
Zoology_2 Ringers Forced out 8

Means and 95% CIs of the raw data

all_hives <- outcome_tally %>%
  group_by(treatment, outcome) %>%
  summarise(n = sum(n)) %>%
  ungroup() %>% mutate(hive = "All hives")

pd <- position_dodge(.3)
outcome_tally %>%
  group_by(treatment, outcome) %>%
  summarise(n = sum(n)) %>% mutate() %>%
  group_by(treatment) %>%
  mutate(total_n = sum(n),
         percent = 100 * n / sum(n),
         SE = sqrt(total_n * (percent/100) * (1-(percent/100)))) %>% 
  ungroup() %>%
  mutate(lowerCI = map_dbl(1:n(), ~ 100 * binom.test(n[.x], total_n[.x])$conf.int[1]),
         upperCI = map_dbl(1:n(), ~ 100 * binom.test(n[.x], total_n[.x])$conf.int[2])) %>%
  filter(outcome != "Stayed inside the hive") %>%
  ggplot(aes(treatment, percent, fill = outcome)) + 
  geom_errorbar(aes(ymin=lowerCI, ymax=upperCI), position = pd, width = 0) + 
  geom_point(stat = "identity", position = pd, colour = "grey15", pch = 21, size = 4) + 
  scale_fill_brewer(palette = "Pastel1", name = "Outcome", direction = -1) + 
  xlab("Treatment") + ylab("% bees (+95% CIs)") + 
  theme(legend.position = "top") + 
  coord_flip()

Version Author Date
1ce9e19 lukeholman 2020-04-21

Multinomial model of outcome

Run the models

Fit a multinomial logisitic model, with 3 possible outcomes describing what happened to each bee introduced to the hive: stayed inside, left of its own volition, or forced out by the other workers. To assess the effects of our predictor variables, we compare 5 models with different fixed factors, ranking them by posterior model probability.

if(!file.exists("output/exp1_model.rds")){
  
  exp1_model_v1 <- brm(
    outcome_numeric ~ treatment * hive + observation_time_minutes, 
    data = data_for_categorical_model, 
    prior = c(set_prior("normal(0, 3)", class = "b", dpar = "mu2"),
              set_prior("normal(0, 3)", class = "b", dpar = "mu3")),
    family = "categorical", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 5000, seed = 1)
  
  exp1_model_v2 <- brm(
    outcome_numeric ~ treatment + hive + observation_time_minutes, 
    data = data_for_categorical_model, 
    prior = c(set_prior("normal(0, 3)", class = "b", dpar = "mu2"),
              set_prior("normal(0, 3)", class = "b", dpar = "mu3")),
    family = "categorical", save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 5000, seed = 1)
  
  exp1_model_v3 <- brm(
    outcome_numeric ~ hive + observation_time_minutes, 
    data = data_for_categorical_model, 
    prior = c(set_prior("normal(0, 3)", class = "b", dpar = "mu2"),
              set_prior("normal(0, 3)", class = "b", dpar = "mu3")),
    family = "categorical",  save_all_pars = TRUE, sample_prior = TRUE,
    chains = 4, cores = 1, iter = 5000, 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(exp1_model_v1,
                                     exp1_model_v2,
                                     exp1_model_v3))) %>%
    arrange(-post_prob)
  
  saveRDS(exp1_model_v2, "output/exp1_model.rds") # save the top model, treatment + hive
  saveRDS(posterior_model_probabilities, "output/exp1_post_prob.rds")
}

exp1_model <- readRDS("output/exp1_model.rds")
posterior_model_probabilities <- readRDS("output/exp1_post_prob.rds")

Fixed effects from the full model

The code chunk below wrangles the raw output of the summary() functions 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).

tableS1 <- get_fixed_effects_with_p_values(exp1_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, "HeatMtreatedLPS", "Heat-treated LPS"),
         Parameter = str_replace_all(Parameter, "observation_time_minutes", "Observation duration (minutes)")) %>%
  arrange(mu) %>%
  select(-mu, -Rhat, -Bulk_ESS, -Tail_ESS) 

names(tableS1)[3:5] <- c("Est. Error", "Lower 95% CI", "Upper 95% CI")

saveRDS(tableS1, file = "figures/tableS1.rds")

tableS1 %>%
  kable(digits = 3) %>% 
  kable_styling(full_width = FALSE) %>%
  pack_rows("% bees leaving voluntarily", 1, 8) %>%
  pack_rows("% bees forced out", 9, 16)
Parameter Estimate Est. Error Lower 95% CI Upper 95% CI p
% bees leaving voluntarily
Intercept -14.866 9.431 -35.346 2.072 0.045 *
Treatment: Ringers 0.658 0.970 -1.395 2.433 0.232
Treatment: Heat-treated LPS 1.298 0.612 0.126 2.530 0.015 *
Treatment: LPS 1.681 0.602 0.532 2.902 0.002 **
hive1 -1.514 2.617 -6.596 3.576 0.281
hive2 3.127 1.480 0.836 6.624 0.001 **
hive3 -1.520 1.602 -4.785 1.564 0.172
Observation duration (minutes) 0.091 0.090 -0.073 0.284 0.148
% bees forced out
Intercept -7.403 6.705 -20.821 5.738 0.134
Treatment: Ringers 0.552 0.453 -0.341 1.445 0.114
Treatment: Heat-treated LPS 1.298 0.406 0.520 2.097 0.000 ***
Treatment: LPS 0.965 0.419 0.161 1.797 0.011 *
hive1 -0.394 2.523 -5.315 4.675 0.437
hive2 -0.115 0.654 -1.392 1.160 0.431
hive3 -0.762 1.518 -3.826 2.200 0.309
Observation duration (minutes) 0.038 0.068 -0.095 0.176 0.288

Table S1: Table summarising the posterior estimates of each fixed effect in the best-fitting model of Experiment 1. This was a multinomial model with three possible outcomes (stay inside, leave voluntarily, be forced out), and so there are two parameter estimates for the intercept and for each predictor in the model. ‘Treatment’ is a fixed factor with four levels, and the effects shown here are expressed relative to the ‘Intact control’ group. ‘Hive’ was also 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 intact control treatment), and the three hive terms represent the deviation from this mean for three of the four hives. Lastly, observation duration was a continuous variable expressed to the nearest minute. 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.

Plotting estimates from the model

Derive prediction from the posterior

new <- expand.grid(treatment = levels(data_for_categorical_model$treatment), 
                   hive = NA,
                   observation_time_minutes = 120)

preds <- fitted(exp1_model, newdata = new, summary = FALSE)
dimnames(preds) <- list(NULL, new[,1], NULL)

plotting_data <- rbind(
  as.data.frame(preds[,, 1]) %>% mutate(outcome = "Stayed inside the hive", posterior_sample = 1:n()),
  as.data.frame(preds[,, 2]) %>% mutate(outcome = "Left voluntarily", posterior_sample = 1:n()),
  as.data.frame(preds[,, 3]) %>% mutate(outcome = "Forced out", posterior_sample = 1:n())) %>%
  gather(treatment, prop, `Intact control`, Ringers, `Heat-treated LPS`, LPS) %>% 
  mutate(outcome = factor(outcome, c("Stayed inside the hive", "Left voluntarily", "Forced out"))) %>%
  as_tibble() %>% arrange(treatment, outcome) 

stats_data <- plotting_data
plotting_data$treatment <- factor(plotting_data$treatment, c("Intact control", "Ringers", "Heat-treated LPS", "LPS"))

Make Figure 1

cols <- c("#34558b", "#4ec5a5", "#ffaf12")

dot_plot <- plotting_data %>%
  mutate(outcome = str_replace_all(outcome, "Stayed inside the hive", "Stayed inside"),
         outcome = factor(outcome, c("Stayed inside", "Left voluntarily", "Forced out"))) %>% 
  ggplot(aes(100 * prop, treatment)) + 
  stat_dotsh(quantiles = 100, fill = "grey40", colour = "grey40") + # aes(fill = treatment), 
  stat_pointintervalh(aes(colour = outcome, fill = outcome), 
                      .width = c(0.5, 0.95),
                      position = position_nudge(y = -0.07), 
                      point_colour = "grey26", pch = 21, stroke = 0.4) + 
  scale_colour_manual(values = cols) + 
  scale_fill_manual(values = cols) + 
  facet_wrap( ~ outcome, scales = "free_x") + 
  xlab("% bees (posterior estimate)") + ylab("Treatment") + 
  theme_bw() + 
  coord_cartesian(ylim=c(1.4, 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 <- stats_data %>%
  spread(treatment, prop) %>%
  mutate(LOR_intact_Ringers = get_log_odds(`Intact control`, Ringers),
         LOR_intact_heat = get_log_odds(`Intact control`, `Heat-treated LPS`),
         LOR_intact_LPS = get_log_odds(`Intact control`, LPS),
         LOR_Ringers_heat = get_log_odds(Ringers, `Heat-treated LPS`),
         LOR_Ringers_LPS = get_log_odds(Ringers, LPS), 
         LOR_heat_LPS = get_log_odds(`Heat-treated LPS`, LPS)) %>%
  select(posterior_sample, outcome, starts_with("LOR")) %>%
  gather(LOR, comparison, starts_with("LOR")) %>%
  mutate(LOR = str_remove_all(LOR, "LOR_"), 
         LOR = str_replace_all(LOR, "heat_LPS", "LPS\n(Heat-treated LPS)"),
         LOR = str_replace_all(LOR, "Ringers_LPS", "LPS\n(Ringers)"),
         LOR = str_replace_all(LOR, "Ringers_heat", "Heat-treated LPS\n(Ringers)"),
         LOR = str_replace_all(LOR, "intact_Ringers", "Ringers\n(Intact control)"),
         LOR = str_replace_all(LOR, "intact_heat", "Heat-treated LPS\n(Intact control)"),
         LOR = str_replace_all(LOR, "intact_LPS", "LPS\n(Intact control)"))

levs <- LOR$LOR %>% unique() %>% sort()
LOR$LOR <- factor(LOR$LOR, rev(levs[c(3,5,4,2,1,6)]))

LOR_plot <- LOR %>%
  mutate(outcome = str_replace_all(outcome, "Stayed inside the hive", "Stayed inside"),
         outcome = factor(outcome, levels = rev(c("Forced out", "Left voluntarily", "Stayed inside")))) %>%
  ggplot(aes(comparison, y = LOR, colour = outcome)) + 
  geom_vline(xintercept = 0, linetype = 2) + 
  geom_vline(xintercept = 0.6931472, linetype = 2, colour = "pink") +
  geom_vline(xintercept = -0.6931472, linetype = 2, colour = "pink") +
  stat_pointintervalh(aes(colour = outcome, fill = outcome), 
                      .width = c(0.5, 0.95),
                      position = position_dodge(0.5), 
                      point_colour = "grey26", pch = 21, stroke = 0.4) + 
  scale_colour_manual(values = cols) + 
  scale_fill_manual(values = cols) + 
  xlab("Effect size (posterior log odds ratio)") + ylab("Treatment (reference)") + 
  theme_bw() +
  theme(
    text = element_text(family = nice_font),
    panel.grid.major.y = element_blank(),
    legend.position = "none"
  ) 


p <- cowplot::plot_grid(plotlist = list(dot_plot, LOR_plot), labels = c("A", "B"),
                   nrow = 2, align = 'v', axis = 'l', rel_heights = c(1.4, 1))
ggsave(plot = p, filename = "figures/fig1.pdf", height = 7, width = 4.7)
p

Version Author Date
1ce9e19 lukeholman 2020-04-21



Figure 1: Panel A shows the posterior estimate of the mean % bees staying inside the hive (left), leaving voluntarily (middle), or being forced out (right), for each of the four treatments. The quantile dot plot shows 100 approximately equally likely estimates of the true % bees, and the horizontal bars show the median and the 50% and 95% credible intervals of the posterior distribution. Panel B gives the posterior estimates of the effect size of each treatment, relative to one of the other treatments (the name of which appears in parentheses), and expressed as a log odds ratio (LOR). Positive LOR indicates that the % bees showing this particular outcome is higher in the treatment than the control; for example, more bees left voluntarily (green) or were forced out (orange) in the LPS treatment than in the intact control. The dashed lines mark \(LOR = 0\), indicating no effect, and \(LOR = \pm log(2)\), i.e. the point at which the odds are twice as high in one treatment as the other. Statistical results associated with this figure are described in Tables S1-S2.

Hypothesis testing and effect sizes

This section calculates the posterior difference in treatment group means, in order to perform some null hypothesis testing, calculate effect size (as a log odds ratio), and calculate the 95% credible intervals on the effect size.

The following code chunks perform planned contrasts between pairs of treatments that we consider important to the biological hypotheses under test. For example the contrast between the LPS treatment and the Ringers treatment provides information about the effect of immmune stimulation, while the Ringers - Intact Control contrast provides information about the effect of wounding in the absence of LPS.

Calculate contrasts: % bees staying inside the hive

# Helper function to summarise a posterior, including calculating
# p_direction, i.e. the posterior probability that the effect size has the stated direction,
# which has a similar interpretation to a one-tailed p-value
my_summary <- function(df, columns) {
  lapply(columns, function(x){

    p <- 1 - (df %>% pull(!! x) %>%
                bayestestR::p_direction() %>% as.numeric())

    df %>% pull(!! x) %>% posterior_summary() %>% as_tibble() %>%
      mutate(p=p) %>% mutate(Metric = x) %>% select(Metric, everything()) %>%
      mutate(` ` = ifelse(p < 0.1, "~", ""),
             ` ` = replace(` `, p < 0.05, "\\*"),
             ` ` = replace(` `, p < 0.01, "**"),
             ` ` = replace(` `, p < 0.001, "***"),
             ` ` = replace(` `, p == " ", ""))
  }) %>% do.call("rbind", .)
}

# Helper to make one unit of the big stats table
make_stats_table <- function(
  dat, groupA, groupB, comparison, 
  metric = "Absolute difference in % bees exiting the hive"){
  
  output <- dat %>%
    spread(treatment, prop) %>%
    mutate(
      metric_here = 100 * (!! enquo(groupA) - !! enquo(groupB)), 
      `Log odds ratio` = get_log_odds(!! enquo(groupB), !! enquo(groupA))) %>%   
    my_summary(c("metric_here", "Log odds ratio")) %>%
    mutate(p = c(" ", format(round(p[2], 4), nsmall = 4)),
           ` ` = c(" ", ` `[2]),
           Comparison = comparison) %>%
    select(Comparison, everything()) %>%
    mutate(Metric = replace(Metric, Metric == "metric_here", metric))
  
  names(output)[names(output) == "metric_here"] <- metric
  output 
}

stayed_inside_stats_table <- rbind(
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Heat-treated LPS`, `LPS`, "LPS (Heat-treated LPS)"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Ringers`, `LPS`, "LPS (Ringers)"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Intact control`, `LPS`, "LPS (Intact control)"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Ringers`, `Heat-treated LPS`, "Heat-treated LPS (Ringers)"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Intact control`, `Heat-treated LPS`, "Heat-treated LPS (Intact control)"),  
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Intact control`, `Ringers`, "Ringers (Intact control)")
  
) %>% as_tibble()

stayed_inside_stats_table[c(2,4,6,8,10,12), 1] <- " "

% bees that left voluntarily

voluntary_stats_table <- rbind(
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Heat-treated LPS`, `LPS`, 
                     "LPS (Heat-treated LPS)", 
                     metric = "Absolute difference in % bees that left voluntarily"),
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `LPS`, 
                     "LPS (Intact control)", 
                     metric = "Absolute difference in % bees that left voluntarily"),
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Ringers`, `LPS`, 
                     "LPS (Ringers)", 
                     metric = "Absolute difference in % bees that left voluntarily"),
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Ringers`, `Heat-treated LPS`, 
                     "Heat-treated LPS (Ringers)", 
                     metric = "Absolute difference in % bees that left voluntarily"),
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `Heat-treated LPS`, 
                     "Heat-treated LPS (Intact control)", 
                     metric = "Absolute difference in % bees that left voluntarily"),

  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `Ringers`, 
                     "Ringers (Intact control)",
                     metric = "Absolute difference in % bees that left voluntarily")
) %>% as_tibble()

voluntary_stats_table[c(2,4,6,8,10,12), 1] <- " "

% bees that were forced out

forced_out_stats_table <- rbind(
  
  stats_data %>%
    filter(outcome == "Forced out") %>%
    make_stats_table(`Heat-treated LPS`, `LPS`, 
                     "LPS (Heat-treated LPS)", 
                     metric = "Absolute difference in % bees that were forced out"),
  stats_data %>%
    filter(outcome == "Forced out") %>%
    make_stats_table(`Intact control`, `LPS`, 
                     "LPS (Intact control)", 
                     metric = "Absolute difference in % bees that were forced out"),
  
  stats_data %>%
    filter(outcome == "Forced out") %>%
    make_stats_table(`Ringers`, `LPS`, 
                     "LPS (Ringers)", 
                     metric = "Absolute difference in % bees that were forced out"),
  stats_data %>%
    filter(outcome == "Forced out") %>%
    make_stats_table(`Ringers`, `Heat-treated LPS`, 
                     "Heat-treated LPS (Ringers)", 
                     metric = "Absolute difference in % bees that were forced out"),  
  stats_data %>%
    filter(outcome == "Forced out") %>%
    make_stats_table(`Intact control`, `Heat-treated LPS`, 
                     "Heat-treated LPS (Intact control)", 
                     metric = "Absolute difference in % bees that were forced out"),
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `Ringers`, "Ringers (Intact control)",
                     metric = "Absolute difference in % bees that were forced out")
) %>% as_tibble()

forced_out_stats_table[c(2,4,6,8,10,12), 1] <- " "

Table S2: This table gives statistics associated with each of the contrasts plotted in Figure 1B. Each pair of rows gives the absolute and standardised effect size (as log odds ratio; LOR) for the focal treatment, relative to the treatment shown in parentheses, for one of the three possible outcomes (stayed inside, left voluntarily, or forced out). A LOR of \(|log(x)|\) indicates that the outcome is \(x\) times more frequent in one treatment compared to the other, e.g. \(|log(2) = 0.69|\) indicates a two-fold difference in frequency. The \(p\) column gives the posterior probability that the true effect size has the same sign as is shown in the Estimate column; this metric has a similar interpretation to a one-tailed \(p\) value in frequentist statistics.

bind_rows(
  stayed_inside_stats_table,
  voluntary_stats_table,
  forced_out_stats_table) %>%
  kable(digits = 2) %>% kable_styling(full_width = FALSE) %>% 
  row_spec(seq(2,36,by=2), extra_css = "border-bottom: solid;") %>%
  pack_rows("% bees staying inside", 1, 12) %>%
  pack_rows("% bees leaving voluntarily", 13, 24) %>%
  pack_rows("% bees forced out", 25, 36)
Comparison Metric Estimate Est.Error Q2.5 Q97.5 p
% bees staying inside
LPS (Heat-treated LPS) Absolute difference in % bees exiting the hive -0.98 8.09 -17.18 17.01
Log odds ratio -0.05 0.43 -0.85 0.90 0.4255
LPS (Ringers) Absolute difference in % bees exiting the hive 9.54 9.87 -5.35 33.80
Log odds ratio 0.62 0.54 -0.33 1.82 0.1047
LPS (Intact control) Absolute difference in % bees exiting the hive 17.27 10.86 1.89 42.03
Log odds ratio 1.23 0.46 0.38 2.21 0.0021 **
Heat-treated LPS (Ringers) Absolute difference in % bees exiting the hive 10.52 9.66 -5.76 31.87
Log odds ratio 0.68 0.51 -0.37 1.69 0.0840 ~
Heat-treated LPS (Intact control) Absolute difference in % bees exiting the hive 18.25 10.72 2.13 40.41
Log odds ratio 1.29 0.40 0.49 2.09 0.0021 **
Ringers (Intact control) Absolute difference in % bees exiting the hive 7.73 8.93 -4.96 29.75
Log odds ratio 0.61 0.54 -0.44 1.70 0.1158
% bees leaving voluntarily
LPS (Heat-treated LPS) Absolute difference in % bees that left voluntarily -3.64 6.63 -22.30 5.35
Log odds ratio -0.46 0.53 -1.52 0.56 0.1919
LPS (Intact control) Absolute difference in % bees that left voluntarily -9.51 11.02 -40.61 -0.13
Log odds ratio -1.53 0.63 -2.77 -0.28 0.0091 **
LPS (Ringers) Absolute difference in % bees that left voluntarily -6.27 10.01 -35.00 5.24
Log odds ratio -0.95 0.90 -2.82 0.64 0.1396
Heat-treated LPS (Ringers) Absolute difference in % bees that left voluntarily -2.64 8.40 -25.56 11.88
Log odds ratio -0.49 0.94 -2.46 1.20 0.3086
Heat-treated LPS (Intact control) Absolute difference in % bees that left voluntarily -5.87 8.33 -30.99 0.48
Log odds ratio -1.07 0.66 -2.38 0.25 0.0546 ~
Ringers (Intact control) Absolute difference in % bees that left voluntarily -3.23 7.79 -26.72 6.36
Log odds ratio -0.58 0.98 -2.37 1.47 0.2559
% bees forced out
LPS (Heat-treated LPS) Absolute difference in % bees that were forced out 4.62 6.30 -4.80 20.93
Log odds ratio 0.39 0.39 -0.36 1.19 0.1601
LPS (Intact control) Absolute difference in % bees that were forced out -7.76 8.27 -28.69 0.83
Log odds ratio -0.80 0.48 -1.71 0.21 0.0535 ~
LPS (Ringers) Absolute difference in % bees that were forced out -3.27 6.31 -19.17 7.38
Log odds ratio -0.30 0.46 -1.18 0.64 0.2446
Heat-treated LPS (Ringers) Absolute difference in % bees that were forced out -7.88 7.87 -27.16 1.34
Log odds ratio -0.69 0.44 -1.53 0.18 0.0556 ~
Heat-treated LPS (Intact control) Absolute difference in % bees that were forced out -12.38 10.49 -36.95 -0.32
Log odds ratio -1.18 0.44 -2.03 -0.29 0.0078 **
Ringers (Intact control) Absolute difference in % bees that were forced out -3.23 7.79 -26.72 6.36
Log odds ratio -0.58 0.98 -2.37 1.47 0.2559

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] cowplot_1.0.0    tidybayes_2.0.1  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