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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(lme4)
library(bayesplot)
library(tidyverse)
library(gridExtra)
library(kableExtra)
library(bayestestR)
library(tidybayes)
library(cowplot)
library(car)
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()

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

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

durations <- bind_rows(durations, tibble(hive = "SkyLab", observation_time_minutes = 90))

# Note that we here merge the heat-treated LPS data with the LPS data. 
# This change was made because there is no difference in the response variables between the two LPS treatments (heated and standard LPS), and because all evidence suggests that heat treatment does not do anything to the LPS; see the earlier version of this paper on bioarXiv for complete results without merging these treatments and discussion of why we included two LPS treatments (short version: immunologists often have heat-treated LPS as a control, even though this does not make any sense because LPS is notoriously heat-stable, and an immunologist colleague told us to include this control before we knew about this). 
# The original manuscript was rejected by 2 journals, in part because the reviewers were baffled by the inclusion of two different LPS treatments, and so we merged the LPS for simplicity in this version. The results are not changed in any way (they're jsut simpler as there are now 3 treatments instead of 4 in experiment 1) - see the bioarXiv version for comparison.
outcome_tally <- read_csv(file = "data/clean_data/experiment_1_outcome_tally.csv") %>%
  mutate(treatment = replace(treatment, treatment == "Heat-treated LPS", "LPS")) %>% # merge the 2 LPS treatments
  group_by(hive, treatment, outcome) %>%
  summarise(n = sum(n), .groups = "drop") %>%
  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)) %>%
  arrange(hive, treatment, outcome)

# 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],
      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")

Inspect the raw data

Click the three tabs to see each table.

Sample sizes by treatment

sample_sizes <- data_for_categorical_model %>%
  group_by(treatment) %>%
  summarise(n = n(), .groups = "drop") 

sample_sizes %>%
  kable() %>% kable_styling(full_width = FALSE)
treatment n
Intact control 321
Ringers 153
LPS 368

Sample sizes by treatment and hive

data_for_categorical_model %>%
  group_by(hive, treatment) %>%
  summarise(n = n(), .groups = "drop") %>%
  spread(treatment, n) %>%
  kable() %>% kable_styling(full_width = FALSE)
hive Intact control Ringers LPS
Garden 77 41 71
SkyLab 105 NA 101
Zoology 106 80 134
Zoology_2 33 32 62

Oberved outcomes

outcome_tally %>%
  spread(outcome, n) %>%
  kable(digits = 3) %>% kable_styling(full_width = FALSE) 
hive treatment Stayed inside the hive Left voluntarily Forced out
Garden Intact control 75 0 2
Garden Ringers 41 0 0
Garden LPS 71 0 0
SkyLab Intact control 102 3 0
SkyLab LPS 82 12 7
Zoology Intact control 105 0 1
Zoology Ringers 74 1 5
Zoology LPS 119 3 12
Zoology_2 Intact control 24 1 8
Zoology_2 Ringers 23 1 8
Zoology_2 LPS 37 3 22

Plot showing raw means and 95% CI of the mean

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

pd <- position_dodge(.3)
outcome_tally %>%
  group_by(treatment, outcome) %>%
  summarise(n = sum(n), .groups = "drop") %>% 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 = "Pastel2", name = "Outcome", direction = -1) + 
  xlab("Treatment") + ylab("% bees (\u00B1 95% CIs)") + 
  theme_bw(20) + 
  theme(legend.position = "top",
        text = element_text(family = nice_font)) + 
  coord_flip()

Version Author Date
3e419d1 lukeholman 2021-04-27
6ee79e9 lukeholman 2020-08-21
f97baee lukeholman 2020-05-02
8c3b471 lukeholman 2020-04-21
1ce9e19 lukeholman 2020-04-21

Preliminary GLMM

The multinomial model below is not commonly used, though we believe it is the right choice for this particular experiment (e.g. because it can model a three-item categorical response variable, and it can incorporate priors). However during peer review, we were asked whether the results were similar when using standard statistical methods. To address this question, we here present a frequentist Generalised Linear Mixed Model (GLMM; using lme4::glmer), which tests the null hypothesis that the proportion of bees exiting the hive (i.e. the proportion leaving voluntarily plus those that were forced out) is equal between treatment groups and hives.

The model’s qualitative results are similar to those from the multinomial model: bees treated with LPS left the hive more often than intact controls (and there was a non-significant trend for more LPS bees to leave than Ringers bees), and there was variation between hives in the proportion of bees leaving.

Parameter estimates from the GLMM

With Intact control as the reference level

Note that the intact and Ringers controls are not different, but the intact control differs from the LPS treatment.

glmm_data <- outcome_tally %>% 
  group_by(hive, treatment, outcome) %>% 
  summarise(n = sum(n)) %>% 
  mutate(left = ifelse(outcome == "Stayed inside the hive", "stayed_inside" ,"left_hive")) %>% 
  group_by(hive, treatment, left) %>% 
  summarise(n = sum(n)) %>%
  spread(left, n) 

simple_model <- glmer(
    cbind(left_hive, stayed_inside) ~ treatment + (1 | hive), 
    data = glmm_data, 
    family = "binomial")

summary(simple_model)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: cbind(left_hive, stayed_inside) ~ treatment + (1 | hive)
   Data: glmm_data

     AIC      BIC   logLik deviance df.resid 
    70.0     71.6    -31.0     62.0        7 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.3801 -0.9123 -0.1932  0.6095  1.9146 

Random effects:
 Groups Name        Variance Std.Dev.
 hive   (Intercept) 1.622    1.273   
Number of obs: 11, groups:  hive, 4

Fixed effects:
                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)       -3.2470     0.7038  -4.614 3.95e-06 ***
treatmentRingers   0.7016     0.4086   1.717   0.0859 .  
treatmentLPS       1.2881     0.3095   4.162 3.16e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) trtmnR
trtmntRngrs -0.260       
treatmntLPS -0.335  0.586

With Ringers as the reference level

Note that the intact and Ringers controls are not different as before. Moreover the Ringers and LPS treatment do not differ significantly.

simple_model <- glmer(
    cbind(left_hive, stayed_inside) ~ treatment + (1 | hive), 
    data = glmm_data %>%
  mutate(treatment = relevel(treatment, ref = "Ringers")), 
    family = "binomial")

summary(simple_model)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: cbind(left_hive, stayed_inside) ~ treatment + (1 | hive)
   Data: glmm_data %>% mutate(treatment = relevel(treatment, ref = "Ringers"))

     AIC      BIC   logLik deviance df.resid 
    70.0     71.6    -31.0     62.0        7 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.3801 -0.9123 -0.1932  0.6095  1.9146 

Random effects:
 Groups Name        Variance Std.Dev.
 hive   (Intercept) 1.622    1.273   
Number of obs: 11, groups:  hive, 4

Fixed effects:
                        Estimate Std. Error z value Pr(>|z|)    
(Intercept)              -2.5454     0.7158  -3.556 0.000377 ***
treatmentIntact control  -0.7016     0.4086  -1.717 0.085946 .  
treatmentLPS              0.5865     0.3383   1.733 0.083022 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
            (Intr) trtmIc
trtmntIntcc -0.315       
treatmntLPS -0.376  0.671

Inspect Type II Anova table

Anova(simple_model, test = "Chisq", Type = "II")
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: cbind(left_hive, stayed_inside)
           Chisq Df Pr(>Chisq)    
treatment 18.115  2  0.0001165 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Baysian multinomial model

Fit the model

Fit the multinomial logistic models, with a 3-item response variable describing what happened to each bee introduced to the hive: stayed inside, left voluntarily, or forced out by the other workers.

if(!file.exists("output/exp1_model.rds")){
  
  prior <- c(set_prior("normal(0, 3)", class = "b", dpar = "mu2"),
             set_prior("normal(0, 3)", class = "b", dpar = "mu3"),
             set_prior("normal(0, 1)", class = "sd", dpar = "mu2", group = "hive"),
             set_prior("normal(0, 1)", class = "sd", dpar = "mu3", group = "hive"))
  
  exp1_model <- brm(
    outcome_numeric ~ treatment + (1 | hive), 
    data = data_for_categorical_model, 
    prior = prior,
    family = "categorical", 
    chains = 4, cores = 1, iter = 5000, seed = 1)
  
  saveRDS(exp1_model, "output/exp1_model.rds") 
}

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

Posterior predictive check

This plot shows ten predictions from the posterior (pale blue) as well as the original data (dark blue), for the three categorical outcomes (1: stayed inside, 2: left voluntarily, 3: forced out). The predicted number of bees in each outcome category is similar to the real data, illustrating that the model is able to recapitulate the original data fairly closely (a necessary requirement for making inferences from the model).

pp_check(exp1_model, type = "hist", nsamples = 8)

Version Author Date
3e419d1 lukeholman 2021-04-27
9ebe5df lukeholman 2021-01-12

Parameter estimates from the model

Output of the Bayesian multinomial logistic model

summary(exp1_model)
 Family: categorical 
  Links: mu2 = logit; mu3 = logit 
Formula: outcome_numeric ~ treatment + (1 | hive) 
   Data: data_for_categorical_model (Number of observations: 842) 
Samples: 4 chains, each with iter = 5000; warmup = 2500; thin = 1;
         total post-warmup samples = 10000

Group-Level Effects: 
~hive (Number of levels: 4) 
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(mu2_Intercept)     1.34      0.51     0.55     2.51 1.00     6513     6060
sd(mu3_Intercept)     1.39      0.43     0.74     2.38 1.00     5443     6887

Population-Level Effects: 
                     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
mu2_Intercept           -4.94      0.93    -6.97    -3.30 1.00     4805     5207
mu3_Intercept           -3.59      0.81    -5.24    -2.00 1.00     3995     5108
mu2_treatmentRingers     0.59      0.97    -1.43     2.38 1.00     9475     6896
mu2_treatmentLPS         1.57      0.56     0.55     2.73 1.00    11154     7439
mu3_treatmentRingers     0.60      0.46    -0.31     1.50 1.00     8390     7922
mu3_treatmentLPS         1.16      0.37     0.46     1.93 1.00     7964     7060

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 S1

The code chunk below wrangles the 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 S1: Table summarising the posterior estimates of each fixed effect in the Bayesian multinomial logistic model of Experiment 1. Because there were three possible outcomes for each bee (Stayed inside, Left voluntarily, or Forced out), there are two parameter estimates for each predictor in the model. ‘Treatment’ is a fixed factor with three levels, and the effects shown here are expressed relative to the ‘Intact control’ group. 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.

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: ")) %>%
  arrange(mu) %>%
  select(-mu, -Rhat, -Bulk_ESS, -Tail_ESS) %>%
  mutate(PP = format(round(PP, 4), nsmall = 4))

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, 3) %>%
  pack_rows("% bees forced out", 4, 6)
Parameter Estimate Est. Error Lower 95% CI Upper 95% CI PP
% bees leaving voluntarily
Intercept -4.937 0.929 -6.969 -3.300 0.0000 ***
Treatment: Ringers 0.590 0.968 -1.426 2.375 0.2570
Treatment: LPS 1.571 0.555 0.555 2.731 0.0007 ***
% bees forced out
Intercept -3.586 0.812 -5.244 -1.999 0.0000 ***
Treatment: Ringers 0.596 0.458 -0.310 1.497 0.0977 ~
Treatment: LPS 1.164 0.369 0.462 1.929 0.0001 ***

Plotting estimates from the model

Derive prediction from the posterior

get_posterior_preds <- function(focal_hive){
  new <- expand.grid(
    treatment = levels(data_for_categorical_model$treatment), 
    hive = focal_hive)
  
  preds <- fitted(exp1_model, newdata = new, summary = FALSE)
  dimnames(preds) <- list(NULL, new[,1], NULL)
  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, LPS) %>% 
    mutate(outcome = factor(outcome, 
                            c("Stayed inside the hive", "Left voluntarily", "Forced out")),
           treatment = factor(treatment, 
                              c("Intact control", "Ringers", "LPS"))) %>%
    as_tibble() %>% arrange(treatment, outcome) 
}

# plotting data for panel A: one specific hive
plotting_data <- get_posterior_preds(focal_hive = "Zoology")

# stats data: for panel B and the table of stats
stats_data <- get_posterior_preds(focal_hive = NA)

Make Figure 1

cols <- RColorBrewer::brewer.pal(3, "Set2")

dot_plot <- plotting_data %>%
  left_join(sample_sizes, by = "treatment") %>%
  arrange(treatment) %>%
  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") + 
  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, 3)) + 
  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_LPS = get_log_odds(`Intact control`, LPS),
         LOR_Ringers_LPS = get_log_odds(Ringers, 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, "Ringers_LPS", "LPS\n(Ringers)"),
         LOR = str_replace_all(LOR, "intact_Ringers", "Ringers\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(y = comparison, x = LOR, colour = outcome)) + 
  geom_hline(yintercept = 0, size = 0.3, colour = "grey20") + 
  geom_hline(yintercept = log(2), linetype = 2, size = 0.6, colour = "grey") +
  geom_hline(yintercept = -log(2), linetype = 2, size = 0.6, colour = "grey") +
  stat_pointinterval(aes(colour = outcome, fill = outcome), 
                     .width = c(0.5, 0.95),
                     position = position_dodge(0.6), 
                     point_colour = "grey26", pch = 21, stroke = 0.4) + 
  scale_colour_manual(values = cols) + 
  scale_fill_manual(values = cols) + 
  ylab("Effect size (log odds ratio)") + 
  xlab("Treatment (reference)") + 
  theme_bw() +
  coord_flip() +
  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 = 1, align = 'v', axis = 'l', 
  rel_heights = c(1.4, 1))
ggsave(plot = p, filename = "figures/fig1.pdf", height = 3.4, width = 9)
p

Version Author Date
3e419d1 lukeholman 2021-04-27
9ebe5df lukeholman 2021-01-12
939ecd0 lukeholman 2021-01-11
eeb5a09 lukeholman 2020-11-30



Figure 1: Results of Experiment 1 (n = 842 bees). 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), 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 (orange) or were forced out (blue) 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.

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

# Helper to make one unit of the big stats table
make_stats_table <- function(
  dat, groupA, groupB, comparison, metric){
  
  output <- dat %>%
    spread(treatment, prop) %>%
    mutate(
      metric_here = 100 * (!! enquo(groupB) - !! enquo(groupA)), 
      `Log odds ratio` = get_log_odds(!! enquo(groupA), !! enquo(groupB))) %>%   
    my_summary(c("metric_here", "Log odds ratio")) %>%
    mutate(PP = c(" ", format(round(PP[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(`Ringers`, `LPS`, "LPS (Ringers)",
                     metric = "Difference in % bees staying inside"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Intact control`, `LPS`, "LPS (Intact control)",
                     metric = "Difference in % bees staying inside"),
  
  stats_data %>%
    filter(outcome == "Stayed inside the hive") %>%
    make_stats_table(`Intact control`, `Ringers`, "Ringers (Intact control)",
                     metric = "Difference in % bees staying inside")
  
) %>% as_tibble()

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

Calculate contrasts: % bees that left voluntarily

voluntary_stats_table <- rbind(
  
  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Ringers`, `LPS`, 
                     "LPS (Ringers)", 
                     metric = "Difference in % bees leaving voluntarily"),
  
   stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `LPS`, 
                     "LPS (Intact control)", 
                     metric = "Difference in % bees leaving voluntarily"),

  stats_data %>%
    filter(outcome == "Left voluntarily") %>%
    make_stats_table(`Intact control`, `Ringers`, 
                     "Ringers (Intact control)",
                     metric = "Difference in % bees leaving voluntarily")
) %>% as_tibble()

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

Calculate contrasts: % bees that were forced out

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

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

Present all contrasts in one table:

Table S2: This table gives statistics associated with each of the contrasts plotted in Figure 1B. Each pair of rows gives the absolute effect size (i.e. the difference in % bees) 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. \(log(2) = 0.69\) and \(log(0.5) = -0.69\) correspond to a two-fold difference in frequency. The \(PP\) 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.

tableS2 <- bind_rows(
  stayed_inside_stats_table,
  voluntary_stats_table,
  forced_out_stats_table) 

saveRDS(tableS2, file = "figures/tableS2.rds")

tableS2 %>%
  kable(digits = 2) %>% kable_styling(full_width = FALSE) %>% 
  row_spec(seq(2,18,by=2), extra_css = "border-bottom: solid;") %>%
  pack_rows("% bees staying inside", 1, 6) %>%
  pack_rows("% bees leaving voluntarily", 7, 12) %>%
  pack_rows("% bees forced out", 13, 18)
Comparison Metric Estimate Est.Error Q2.5 Q97.5 PP
% bees staying inside
LPS (Ringers) Difference in % bees staying inside -6.50 6.26 -22.41 1.41
Log odds ratio -0.65 0.42 -1.52 0.14 0.0516 ~
LPS (Intact control) Difference in % bees staying inside -11.22 8.64 -31.40 -1.03
Log odds ratio -1.27 0.35 -2.00 -0.60 0.0000 ***
Ringers (Intact control) Difference in % bees staying inside -4.72 5.83 -20.54 1.53
Log odds ratio -0.62 0.48 -1.59 0.30 0.0902 ~
% bees leaving voluntarily
LPS (Ringers) Difference in % bees leaving voluntarily 2.26 3.37 -2.86 10.72
Log odds ratio 0.92 0.88 -0.63 2.79 0.1392
LPS (Intact control) Difference in % bees leaving voluntarily 3.53 3.45 0.08 12.40
Log odds ratio 1.46 0.57 0.42 2.64 0.0029 **
Ringers (Intact control) Difference in % bees leaving voluntarily 1.27 2.91 -1.97 9.71
Log odds ratio 0.55 0.97 -1.46 2.33 0.2716
% bees forced out
LPS (Ringers) Difference in % bees forced out 4.24 5.60 -1.24 20.39
Log odds ratio 0.54 0.37 -0.18 1.29 0.0743 ~
LPS (Intact control) Difference in % bees forced out 7.69 8.14 0.54 28.33
Log odds ratio 1.12 0.37 0.41 1.89 4e-04 ***
Ringers (Intact control) Difference in % bees forced out 1.27 2.91 -1.97 9.71
Log odds ratio 0.55 0.97 -1.46 2.33 0.2716

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.7

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_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8

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

other attached packages:
 [1] car_3.0-8        carData_3.0-4    cowplot_1.0.0    tidybayes_2.0.3  bayestestR_0.6.0 kableExtra_1.3.4
 [7] gridExtra_2.3    forcats_0.5.0    stringr_1.4.0    dplyr_1.0.0      purrr_0.3.4      readr_1.3.1     
[13] tidyr_1.1.0      tibble_3.0.1     ggplot2_3.3.2    tidyverse_1.3.0  bayesplot_1.7.2  lme4_1.1-23     
[19] Matrix_1.2-18    brms_2.14.4      Rcpp_1.0.4.6     showtext_0.9-1   showtextdb_3.0   sysfonts_0.8.2  
[25] workflowr_1.6.2 

loaded via a namespace (and not attached):
  [1] readxl_1.3.1         backports_1.1.7      systemfonts_0.2.2    plyr_1.8.6           igraph_1.2.5        
  [6] svUnit_1.0.3         splines_4.0.3        crosstalk_1.1.0.1    TH.data_1.0-10       rstantools_2.1.1    
 [11] inline_0.3.15        digest_0.6.25        htmltools_0.5.0      rsconnect_0.8.16     fansi_0.4.1         
 [16] magrittr_2.0.1       openxlsx_4.1.5       modelr_0.1.8         RcppParallel_5.0.1   matrixStats_0.56.0  
 [21] svglite_1.2.3        xts_0.12-0           sandwich_2.5-1       prettyunits_1.1.1    colorspace_1.4-1    
 [26] blob_1.2.1           rvest_0.3.5          haven_2.3.1          xfun_0.22            callr_3.4.3         
 [31] crayon_1.3.4         jsonlite_1.7.0       survival_3.2-7       zoo_1.8-8            glue_1.4.2          
 [36] gtable_0.3.0         emmeans_1.4.7        webshot_0.5.2        V8_3.4.0             pkgbuild_1.0.8      
 [41] rstan_2.21.2         abind_1.4-5          scales_1.1.1         mvtnorm_1.1-0        DBI_1.1.0           
 [46] miniUI_0.1.1.1       viridisLite_0.3.0    xtable_1.8-4         foreign_0.8-80       stats4_4.0.3        
 [51] StanHeaders_2.21.0-3 DT_0.13              htmlwidgets_1.5.1    httr_1.4.1           threejs_0.3.3       
 [56] RColorBrewer_1.1-2   arrayhelpers_1.1-0   ellipsis_0.3.1       farver_2.0.3         pkgconfig_2.0.3     
 [61] loo_2.3.1            dbplyr_1.4.4         labeling_0.3         tidyselect_1.1.0     rlang_0.4.6         
 [66] reshape2_1.4.4       later_1.0.0          munsell_0.5.0        cellranger_1.1.0     tools_4.0.3         
 [71] cli_2.0.2            generics_0.0.2       broom_0.5.6          ggridges_0.5.2       evaluate_0.14       
 [76] fastmap_1.0.1        yaml_2.2.1           processx_3.4.2       knitr_1.32           fs_1.4.1            
 [81] zip_2.1.1            nlme_3.1-149         whisker_0.4          mime_0.9             projpred_2.0.2      
 [86] xml2_1.3.2           compiler_4.0.3       shinythemes_1.1.2    rstudioapi_0.11      curl_4.3            
 [91] gamm4_0.2-6          reprex_0.3.0         statmod_1.4.34       stringi_1.5.3        highr_0.8           
 [96] ps_1.3.3             Brobdingnag_1.2-6    gdtools_0.2.2        lattice_0.20-41      nloptr_1.2.2.1      
[101] markdown_1.1         shinyjs_1.1          vctrs_0.3.0          pillar_1.4.4         lifecycle_0.2.0     
[106] bridgesampling_1.0-0 estimability_1.3     data.table_1.12.8    insight_0.8.4        httpuv_1.5.3.1      
[111] R6_2.4.1             promises_1.1.0       rio_0.5.16           codetools_0.2-16     boot_1.3-25         
[116] colourpicker_1.0     MASS_7.3-53          gtools_3.8.2         assertthat_0.2.1     rprojroot_1.3-2     
[121] withr_2.2.0          shinystan_2.5.0      multcomp_1.4-13      mgcv_1.8-33          parallel_4.0.3      
[126] hms_0.5.3            grid_4.0.3           coda_0.19-3          minqa_1.2.4          rmarkdown_2.5       
[131] git2r_0.27.1         shiny_1.4.0.2        lubridate_1.7.8      base64enc_0.1-3      dygraphs_1.1.1.6