🤖 AI Summary
This study addresses bias in marginal population parameter estimation for non-normal, bivariate correlated data—particularly in longitudinal settings. We systematically compare the performance of generalized joint regression models (GJRM), generalized linear mixed models (GLMM), and generalized estimating equations (GEE). Through Monte Carlo simulations and analysis of real-world physician visit data, we first demonstrate that GLMM yields substantial bias in marginal parameter estimates under non-identity link functions and skewed response distributions. In contrast, GJRM—when the copula is correctly specified—exhibits unbiased marginal estimation, robust standard errors, and superior model fit. GJRM maintains consistency of marginal estimates and validity of statistical inference across diverse non-normal distributions (e.g., Poisson, negative binomial, Beta), outperforming GLMM, GEE, and generalized linear models (GLM). These findings establish GJRM as a more reliable methodological choice for analyzing such complex correlated data.
📝 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.