A comparison between copula-based, mixed model, and estimating equation methods for analysis of bivariate correlated data (2410.11892v2)

Abstract: Regression analysis of non-normal correlated data is commonly performed using generalized linear mixed models (GLMM) and generalized estimating equations (GEE). The recent development of generalized joint regression models (GJRM) provide an alternative to these approaches by using copulas to flexibly model response variables and their dependence structures. This paper presents a simulation study comparing GJRM with alternative methods. We find that for the normal model with identity link, all models provide accurate estimates of marginal population parameters with comparable fit. However, for non-normal marginal distributions and when a non-identity link function is used, we highlight a major pitfall in the use of GLMMs: without significant adjustment they provide highly biased estimates of marginal population parameters. GLMM bias is more pronounced when the marginal distributions are more skewed or highly correlated. In addition, we highlight discrepancies between the estimates from different GLMM packages. In contrast, we find that GJRM provides unbiased estimates across all distributions with accurate standard errors when the copula is correctly specified. In addition, we highlight the advantages of the likelihood-based structure of the GJRM and show that it provides a model fit comparable, and often favorable to, GLMMs and GLMs. In a longitudinal study of doctor visits, we show that the GJRM provides better model fits than a comparable non-GAMLSS GLMM, GEE or GLM, due to its greater selection of marginal distributions. We conclude that the GJRM provides a superior approach to current popular models for regression of non-normal correlated data when population parameters are of interest.