Empirical performance of parameter estimation methods in multivariate generalized linear mixed effect models with application to ecological data

Abstract

This study compares two parameter estimation methods for Multivariate Generalized Linear Mixed Models (MGLMMs): Bayesian Markov Chain Monte Carlo (MCMC</>) and frequentist Gaussian Hermite Quadrature (GHQ). Using simulations, we examined their performance across varying response distributions, sample sizes, random effect variances, and between-variable correlations. MCMC performed better for Poisson and mixed distributions, while GHQ outperformed in terms of Gaussian responses with medium random effect variance. Both methods showed a reduced accuracy with increasing sample size, random effect variance, and correlations. Results obtained were validated using ecological data.