glmernb

glmer.nb is a function in the R package lme4 that fits generalized linear mixed models (GLMMs) with a negative binomial response. It is used for count data that show overdispersion relative to a Poisson model, providing a way to model both fixed effects and random effects within the GLMM framework.

In a glmer.nb model, the conditional mean mu is linked to the linear predictor through a log link, with mu_ij = exp(X_ij beta + Z_ij b), where X and Z are design matrices for fixed and random effects, respectively. The response Y_ij is assumed to follow a negative binomial distribution with a dispersion parameter theta, which is estimated from the data together with the fixed-effect coefficients beta and the variance components for the random effects. Random effects are typically assumed to be normally distributed with a specified covariance structure.

Estimation is performed by maximum likelihood with numerical integration over the random effects, commonly using the Laplace approximation. The function returns an object of class merMod, containing parameter estimates, standard errors, and diagnostic information. It supports common GLMM features such as multiple random effects terms and crossed or nested grouping factors.

Practical use involves comparing glmer.nb to Poisson-based models to assess overdispersion and model fit, often via information criteria (AIC, BIC) or likelihood ratio tests. Limitations include potential convergence difficulties and longer computation times for complex models or large datasets. For greater flexibility or alternative parameterizations of the negative binomial family, researchers may consider other packages such as glmmTMB or brms, which offer broader modeling options for NB-based GLMMs.

See also: glmer, lme4, negative binomial models, glmmTMB, brms.