求助：在R中使用glmmadmb验证negative binomial glmm的模型假设

Got it, let's break down how to verify that your negative binomial generalized linear mixed model (GLMM) fits the necessary assumptions—critical for trusting your results, especially with your dataset spanning 28 streams across 7 reserves and 4 land use types. Here's a step-by-step guide tailored to your setup:

Key Assumptions & How to Test Them #

1. Your response variable fits the negative binomial distribution #

Negative binomial models are designed for count data (non-negative integers) with overdispersion (variance > mean). First confirm:

• Your response is count data (e.g., number of trail segments per stream, not just presence/absence—if it's yes/no, you'd need a binomial model instead).
• Calculate mean vs. variance to confirm overdispersion:

  # Replace with your actual column names
  mean_trails <- mean(your_dataset$trail_count)
  var_trails <- var(your_dataset$trail_count)
  cat("Mean:", mean_trails, "\nVariance:", var_trails)
  

  If variance is noticeably larger than the mean, negative binomial is the right call over Poisson.

2. Residuals are independent (except for accounted random effects) #

Since you're using a mixed model, you should already be accounting for clustering from your 7 reserves (and possibly streams nested within reserves). To double-check:

• Plot residuals against data collection order or spatial coordinates (streams are geographic, so spatial autocorrelation is a risk):

  model_resids <- residuals(your_glmm_model)
  # Plot against spatial x-coordinate (adjust to your data)
  plot(your_dataset$x_coord, model_resids, xlab = "Spatial X", ylab = "Residuals")
  abline(h = 0, col = "red")
  

  No clear pattern (e.g., clusters, upward/downward trends) means independence holds. If you see a pattern, you might need to add a spatial random effect.

3. Linear relationship on the log link scale #

Negative binomial GLMMs assume predictors have a linear relationship with the log of the expected count. Test this for continuous predictors using partial residuals:

library(visreg)
# Replace "your_predictor" with a continuous variable (e.g., stream length)
visreg(your_glmm_model, "your_predictor", type = "residuals")

If the points are randomly scattered around zero with no curved pattern, the linearity assumption holds. If not, consider adding a polynomial term or transforming the predictor.

4. No influential outliers #

With 28 streams, outliers can disproportionately affect results. Check using Cook's distance and studentized residuals:

# Cook's distance (measures influence of each observation)
plot(cooks.distance(your_glmm_model), ylab = "Cook's Distance")
abline(h = 4/nrow(your_dataset), col = "red")  # Rule of thumb cutoff

# Studentized residuals
plot(rstudent(your_glmm_model), ylab = "Studentized Residuals")
abline(h = c(-3, 3), col = "red")

Points above the Cook's distance cutoff or outside ±3 for studentized residuals need investigation (e.g., data entry errors, unique stream characteristics).

5. Random effects are normally distributed #

Your random effects (e.g., variation across reserves) should follow a normal distribution. Extract and plot them with a Q-Q plot:

library(lme4)
# Replace "reserve" with your random effect grouping variable
ranef_vals <- ranef(your_glmm_model)$reserve[,1]
qqnorm(ranef_vals, main = "Q-Q Plot of Random Effects")
qqline(ranef_vals, col = "red")

If points fall roughly along the straight line, the normality assumption is satisfied.

6. Overdispersion is properly addressed #

Even with negative binomial, confirm the model has handled overdispersion:

library(MuMIn)
overdispersion <- overdisp_fun(your_glmm_model)
cat("Overdispersion parameter:", overdispersion$dispersion)

A value close to 1 means overdispersion is well-managed. If it's much larger than 1, you might need a zero-inflated negative binomial model (if you have excess zeros) or re-examine your predictor set.

Once you've worked through these checks, you'll have a clear picture of whether your negative binomial GLMM is appropriate for your data. If you hit specific snags (e.g., odd residual patterns, extreme overdispersion), feel free to share your model formula or output for more targeted help!

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