如何在glmmTMB中为关系型数据定义相关结构？

No, glmmTMB does not natively support the MLPE (Modular Linear Predictor Expansion) correlation structure provided by the corMLPE package. However, you can model the non-independence of pairs sharing populations using random effects for individual populations, which achieves a similar goal of accounting for shared population effects.

Alternative Approach: Node-level Random Effects #

Since your dyadic data (population pairs) exhibit dependence when pairs share a common population, you can add random intercepts for each population in both the main and zero-inflation components of the glmmTMB model. This will create covariance between pairs that share either P1 or P2, mirroring the correlation structure captured by corMLPE.

Modified glmmTMB Code #

library(glmmTMB)

# Fit zero-inflated binomial model with population random effects
fit3 <- glmmTMB(
  m ~ pred + (1|P1) + (1|P2),  # Main model: fixed effect of pred + random intercepts for P1 and P2
  zi = ~pred + (1|P1) + (1|P2),  # Zero-inflation component: same structure (adjust if needed)
  data = d,
  family = binomial,
  weights = N.pair
)

summary(fit3)

Key Notes: #

• The terms (1|P1) and (1|P2) add random intercepts for each population in both the main (success probability) and zero-inflation (excess zero probability) parts of the model. This ensures that pairs sharing a population have correlated residuals, accounting for non-independence.
• If you don't expect the zero-inflation component to depend on population-level variation, you can simplify the zero-inflation formula to zi = ~pred (without random effects). Adjust based on your biological hypotheses.
• Check model convergence using convergence(fit3) or by inspecting the random effects variances (if variances are estimated as near-zero, you may need to simplify the model).
• Use the DHARMa package to simulate residuals and verify that the model adequately accounts for non-independence:

  library(DHARMa)
  sim_res <- simulateResiduals(fit3)
  plot(sim_res)
  

Why This Works #

The random effects approach models the dependence between pairs by assigning each population a random deviation from the overall mean. Pairs sharing a population will inherit that population's random effect, leading to correlation between those pairs. This is a standard method for handling dyadic dependence in mixed-effects models and is compatible with glmmTMB's zero-inflated binomial framework.

Alternative: brms (if flexible) #

If you're open to using Bayesian models, the brms package supports custom correlation structures (including MLPE via the cor_mlpe function) alongside zero-inflated binomial models. However, this requires a Bayesian workflow rather than frequentist inference.

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