Random effects’ distribution assumption on joint mixed modelling

Özdemir, Celal Oğuz
Joint mixed model is an appealing approach in medical research where it is critical to estimate the odds of a fatal complication that occurs to a patient given the covariate profile such as a risk factor observed over time. For this kind of estimation, joint mixed model is used. In the standard Bayesian analysis of the model, the error variance and random effects’ variance-covariance matrix are apriori modeled independently with Inverse-Gamma and Inverse-Wishart distributions respectively. Recently however, it is shown that joint apriori modeling via Generalized Multivariate Log-Gamma (G-MVLG) distribution is more efficient than the standard Bayesian analysis for these variance components. Our current aim is to inverstigate the robustness of G-MVLG based and standard analysis to random effects’ distributions. Bivariate Gamma, Bivariate Skew-Normal, Normal distribution and their mixture distributions were considered for the true distribution of random effects. Results show that the G-MVLG approach is robust to the underlying true distribution of random effects when the sample size is sufficiently large. For small samples, a robust approach. Simulations and real data study show that DPP for the random effects distributions is less biased and more efficient.