Hey there! Let's tackle the residual pattern issue you're seeing with your binomial GLM. You've already ruled out influential points via Cook's distance, and since your predictor is categorical (can't transform it), we need to look at other angles to fix the model assumptions. Here are actionable steps to try:

1. Incorporate the courtship_count Predictor #

Your dataset includes courtship_count, a count variable that's likely tied to the probability of mating—more courtships might mean higher mating success! Omitting this could be exactly why your residuals show a pattern: your current model isn't capturing this key source of variation.

Try updating your model to include it (or a transformed version if the count is skewed):

# Basic model with courtship_count added
fitmating_updated <- glm(mating ~ treatment + courtship_count, 
                         family = binomial(link = logit), 
                         data = datafig4)

# Log-transformed version (add 1 to avoid log(0) for zero counts)
fitmating_log <- glm(mating ~ treatment + log(courtship_count + 1), 
                     family = binomial(link = logit), 
                     data = datafig4)

After fitting, recheck your Pearson residuals—this often resolves residual patterns by accounting for unmodeled variation.

2. Check for Overdispersion #

Binomial GLMs assume variance equals mean, but overdispersion (variance > mean) is common with binary data and can cause residual patterns. Calculate the overdispersion parameter first:

overdispersion_param <- sum(residuals(fitmating, type = "pearson")^2) / fitmating$df.residual
print(overdispersion_param)

If this value is much larger than 1 (e.g., >1.5), use a quasibinomial model to adjust for extra variance:

fitmating_quasi <- glm(mating ~ treatment, 
                       family = quasibinomial(link = logit), 
                       data = datafig4)

Quasibinomial models adjust standard errors to account for overdispersion, which can fix residual patterns and give more reliable inference.

3. Diagnose the Exact Residual Pattern #

Before jumping to fixes, take a closer look at what the residual pattern is telling you. Plot residuals against fitted values and courtship_count to identify clear trends:

# Residuals vs fitted probabilities
plot(fitted(fitmating), residuals(fitmating, type = "pearson"),
     xlab = "Fitted Probabilities", ylab = "Pearson Residuals")
abline(h = 0, col = "red", lwd = 2)

# Residuals vs courtship count
plot(datafig4$courtship_count, residuals(fitmating, type = "pearson"),
     xlab = "Courtship Count", ylab = "Pearson Residuals")
abline(h = 0, col = "red", lwd = 2)

If residuals correlate with courtship_count, that's a clear sign this variable needs to be in your model.

4. Non-Parametric or Exact Test Alternatives #

If GLM assumptions still aren't met, you can supplement or replace the GLM with non-parametric tests tailored to your categorical treatment and binary response:

• Fisher's Exact Tests: Compare each treatment group to the control (adjust p-values for multiple comparisons, e.g., Bonferroni):

  control_subset <- subset(datafig4, treatment == "control")
  for (trt in levels(datafig4$treatment)[-1]) {
    trt_subset <- subset(datafig4, treatment == trt)
    contingency_table <- matrix(
      c(sum(control_subset$mating), nrow(control_subset) - sum(control_subset$mating),
        sum(trt_subset$mating), nrow(trt_subset) - sum(trt_subset$mating)),
      nrow = 2
    )
    test_result <- fisher.test(contingency_table)
    cat(sprintf("Treatment: %s | p-value: %.4f\n", trt, test_result$p.value))
  }
  

• Pearson's Chi-Squared Test: If expected cell counts are large enough, test the overall association between treatment and mating:

  chisq_result <- chisq.test(table(datafig4$treatment, datafig4$mating))
  print(chisq_result)
  

5. Check for Hidden Clustering #

If your observations within treatment groups aren't truly independent (e.g., same batch of subjects, shared environment), you might need a mixed-effects model to account for grouping. If you have a grouping variable (even if not explicitly stated), use glmer from the lme4 package:

library(lme4)
# Replace `group_var` with your actual grouping variable if available
fitmating_mixed <- glmer(mating ~ treatment + (1 | group_var),
                         family = binomial,
                         data = datafig4)

Start with step 1 (adding courtship_count)—it's the most straightforward fix given your dataset, and it's likely the missing piece causing residual patterns.

内容的提问来源于stack exchange，提问作者Sam Vanbergen