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Load data and R packages

library(showtext)
library(brms)
library(bayesplot)
library(tidyverse)
library(gridExtra)
library(kableExtra)
library(bayestestR)
library(cowplot)
library(tidybayes)
library(scales)
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()

experiment3 <- read_csv("data/clean_data/experiment_3.csv")

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

Inspect the raw data

Sample sizes by treatment

sample_sizes <- expt3_counts %>%
  group_by(treatment) %>%
  summarise(n = n(), .groups = "drop") 

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

Sample sizes by treatment and hive

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

Means and standard errors

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

Histogram of the results

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

histo_data <- expt3_counts %>%
  left_join(sample_sizes, by = "treatment") %>%
  arrange(treatment)

raw_histogram <- histo_data %>% 
  filter(grepl("Ringers", treatment)) %>%
  ggplot(aes(100 * percent, 
             fill = treatment)) + 
  geom_histogram(data = histo_data %>% 
                   filter(grepl("LPS", treatment)), 
                 mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, colour = "black", linetype = 2) +
  geom_histogram(mapping = aes(y = ..density..), 
                 alpha = 0.5, bins = 11, 
                 colour = "black") + 
  scale_fill_brewer(palette = "Set1", 
                    direction = 1, name = "Treatment") + 
  xlab("% Time in close contact") + ylab("Frequency") + 
  theme_bw() + 
  theme(legend.position = c(0.17, 0.82),
        legend.background = element_rect(fill = scales::alpha('white', 0.7)),
        text = element_text(family = nice_font)) 

rm(histo_data)
raw_histogram

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Bayesian binomial model of time spent in contact

Run the models

Fit a binomial GLMM where the response is either a 0 (if bees were not in contact) or 1 (if they were). Hive is treated as a fixed factor (to aid model convergence) and the ID of each pair of bees is treated as a random factor (to account for repeated measurements of each pair).

if(!file.exists("output/exp3_model.rds")){
  
  prior <- c(set_prior("normal(0, 3)", class = "b"),
             set_prior("normal(0, 1)", class = "sd", group = "pairID"))
  
  exp3_model <- brm(
    n_touching | trials(n) ~ treatment + hive + (1 | pairID), 
    data = expt3_counts %>% mutate(n = n_touching + n_not_touching), 
    prior = prior,
    family = "binomial", 
    chains = 4, cores = 1, iter = 20000, seed = 1)
  
  saveRDS(exp3_model, "output/exp3_model.rds") 
}
exp3_model <- readRDS("output/exp3_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 proportion of time spent in close contact (0-100%). The predicted time in contact 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(exp3_model, nsamples = 20)

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Fixed effects from the top model

Raw output of the treatment + hive model

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

Group-Level Effects: 
~pairID (Number of levels: 439) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     2.01      0.08     1.86     2.17 1.00     4273     7021

Population-Level Effects: 
             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept        1.67      0.14     1.39     1.94 1.00     1542     3127
treatmentLPS    -0.37      0.20    -0.75     0.02 1.00     1559     3300
hive1           -0.20      0.18    -0.55     0.15 1.00     1585     3238
hive2            0.14      0.16    -0.17     0.46 1.00     1357     3388
hive3           -0.23      0.18    -0.58     0.12 1.00     1438     2609

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

Formatted brms output for Table S5

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


Table S5: Table summarising the posterior estimates of each fixed effect in the model of Experiment 3 (a binomial GLMM where the response variable was 0 when bees were not in close contact, and 1 when they were). ‘Treatment’ is a fixed factor with two levels, and the effect of LPS shown here is expressed relative to the ‘Ringers’ treatment. ‘Hive’ was a fixed factor with four levels (modelled using deviation coding). The model also included one random effect, ‘pair ID’, which grouped observations made on each pair of bees, preventing pseudoreplication. The \(PP\) column gives the posterior probability that the true effect size is opposite in sign to what is reported in the Estimate column, similarly to a \(p\)-value.

tableS5 <- get_fixed_effects_with_p_values(exp3_model) %>% 
  mutate(mu = map_chr(str_extract_all(Parameter, "mu[:digit:]"), ~ .x[1]),
         Parameter = str_remove_all(Parameter, "mu[:digit:]_"),
         Parameter = str_replace_all(Parameter, "treatment", "Treatment: "),
         Parameter = str_replace_all(Parameter, "observation_time_minutes", "Observation duration (minutes)")) %>%
  arrange(mu) %>%
  select(-mu, -Rhat, -Bulk_ESS, -Tail_ESS) %>%
    mutate(PP = format(round(PP, 4), nsmall = 4))

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

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

tableS5 %>%
  kable(digits = 3) %>% 
  kable_styling(full_width = FALSE) 
Parameter Estimate Est. Error Lower 95% CI Upper 95% CI PP
Intercept 1.669 0.141 1.392 1.945 0.0000 ***
Treatment: LPS -0.368 0.197 -0.752 0.024 0.0322 *
hive1 -0.197 0.178 -0.549 0.147 0.1343
hive2 0.143 0.162 -0.175 0.464 0.1860
hive3 -0.227 0.178 -0.579 0.116 0.0999 ~

Plotting estimates from the model

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

panel_c_colour <- "#CC79A7"

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

p <- cowplot::plot_grid(raw_histogram, 
                        dot_plot, labels = c("A", "B"),
                        nrow = 1, align = 'h', axis = 'l')
ggsave(plot = p, filename = "figures/fig3.pdf", height = 3.4, width = 9)
p

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9ebe5df lukeholman 2021-01-12

Figure 3: Results of Experiment 3 (n = 439 bees). 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.

Hypothesis testing and effect sizes

Table S6: Pairs in which one bee had received LPS were observed in close contact less frequently than pairs in which one bee had received Ringers. The \(PP\) 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.

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(PP=p, 
           Metric = c("Absolute difference in % time in close contact", 
                      "Log odds ratio")) %>% 
      select(Metric, everything()) %>%
    mutate(PP = format(round(PP, 4), nsmall = 4))
  output$PP[1] <- " "
  output
}

tableS6 <- 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(PP < 0.05, "\\*", ""),
         ` ` = replace(` `, PP < 0.01, "**"),
         ` ` = replace(` `, PP < 0.001, "***"),
         ` ` = replace(` `, PP == " ", "")) 

saveRDS(tableS6, "figures/tableS6.rds")

tableS6 %>%
  kable(digits = 3) %>% kable_styling() 
Metric Estimate Est.Error Q2.5 Q97.5 PP
Absolute difference in % time in close contact 5.548 2.997 -0.352 11.454
Log odds ratio -0.368 0.197 -0.752 0.024 0.0322 *

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     scales_1.1.1      tidybayes_2.0.3   cowplot_1.0.0     bayestestR_0.11.5
 [7] kableExtra_1.3.4  gridExtra_2.3     forcats_0.5.0     stringr_1.4.0     dplyr_1.0.0       purrr_0.3.4      
[13] readr_2.0.0       tidyr_1.1.0       tibble_3.0.1      ggplot2_3.3.2     tidyverse_1.3.0   bayesplot_1.7.2  
[19] brms_2.14.4       Rcpp_1.0.4.6      showtext_0.9-2    showtextdb_3.0    sysfonts_0.8.3    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       tzdb_0.1.2           modelr_0.1.8         RcppParallel_5.0.1  
 [21] matrixStats_0.56.0   vroom_1.5.3          svglite_1.2.3        xts_0.12-0           sandwich_2.5-1      
 [26] prettyunits_1.1.1    colorspace_1.4-1     blob_1.2.1           rvest_0.3.5          haven_2.3.1         
 [31] xfun_0.26            callr_3.4.3          crayon_1.3.4         jsonlite_1.7.0       lme4_1.1-23         
 [36] survival_3.2-7       zoo_1.8-8            glue_1.4.2           gtable_0.3.0         emmeans_1.4.7       
 [41] webshot_0.5.2        V8_3.4.0             pkgbuild_1.0.8       rstan_2.21.2         abind_1.4-5         
 [46] mvtnorm_1.1-0        DBI_1.1.0            miniUI_0.1.1.1       viridisLite_0.3.0    xtable_1.8-4        
 [51] bit_1.1-15.2         foreign_0.8-80       stats4_4.0.3         StanHeaders_2.21.0-3 DT_0.13             
 [56] datawizard_0.2.1     htmlwidgets_1.5.1    httr_1.4.1           threejs_0.3.3        RColorBrewer_1.1-2  
 [61] arrayhelpers_1.1-0   ellipsis_0.3.1       farver_2.0.3         pkgconfig_2.0.3      loo_2.3.1           
 [66] dbplyr_1.4.4         labeling_0.3         tidyselect_1.1.0     rlang_0.4.6          reshape2_1.4.4      
 [71] later_1.0.0          munsell_0.5.0        cellranger_1.1.0     tools_4.0.3          cli_2.0.2           
 [76] generics_0.0.2       broom_0.5.6          ggridges_0.5.2       evaluate_0.14        fastmap_1.0.1       
 [81] yaml_2.2.1           bit64_0.9-7          processx_3.4.2       knitr_1.32           fs_1.4.1            
 [86] zip_2.1.1            nlme_3.1-149         whisker_0.4          mime_0.9             projpred_2.0.2      
 [91] xml2_1.3.2           rstudioapi_0.11      compiler_4.0.3       shinythemes_1.1.2    curl_4.3            
 [96] gamm4_0.2-6          reprex_0.3.0         statmod_1.4.34       stringi_1.5.3        highr_0.8           
[101] ps_1.3.3             Brobdingnag_1.2-6    gdtools_0.2.2        lattice_0.20-41      Matrix_1.2-18       
[106] nloptr_1.2.2.1       markdown_1.1         shinyjs_1.1          vctrs_0.3.0          pillar_1.4.4        
[111] lifecycle_0.2.0      jquerylib_0.1.1      bridgesampling_1.0-0 estimability_1.3     data.table_1.12.8   
[116] insight_0.14.5       httpuv_1.5.3.1       R6_2.4.1             promises_1.1.0       rio_0.5.16          
[121] codetools_0.2-16     boot_1.3-25          colourpicker_1.0     MASS_7.3-53          gtools_3.8.2        
[126] assertthat_0.2.1     rprojroot_1.3-2      withr_2.2.0          shinystan_2.5.0      multcomp_1.4-13     
[131] mgcv_1.8-33          parallel_4.0.3       hms_0.5.3            grid_4.0.3           coda_0.19-3         
[136] minqa_1.2.4          rmarkdown_2.11       git2r_0.27.1         shiny_1.4.0.2        lubridate_1.7.10    
[141] base64enc_0.1-3      dygraphs_1.1.1.6