Bayesian modelling of mixed outcome types using random effect.

The problem of analyzing associated outcomes of mixed type arises frequently in practice. In this dissertation we develop several Bayesian models for analyzing associated discrete and continuous responses simultaneously using random effects. We also extend these models to overcome the bias in parameter estimation due to ignorance of skewness of the continuous response, a misclassified covariate, and a zero-inflated discrete response. Simulation studies indicate that our models provide good estimates of regression coefficients, response variability, and the correlation between responses. We also show that ignoring the random effects leads to a bias in parameter estimates which is magnified with increasing variability of the random effect. Comparison to corresponding likelihood methods suggests that the Bayesian Poisson-normal (PN) model takes clear advantage of prior information when available, and performs similarly when relatively non-informative priors are used. A Bayesian sample size determination method is also developed. We make three extensions to the PN model accounting for three complications common to Poisson-normal (PN) regression: continuous responses exhibiting skewness, potential misclassification in a binary covariate (MisPSN model), and excess zeros in the Poisson counts (ZipPSN model). Simulation studies are performed for these models, and the results show that ignoring these complications result in estimated regression coefficients further from the truth when compared to the models that accounted for these complications. For the MisPSN model, we study the attenuation of the regression parameters caused by the misclassified covariate. For the ZipPSN model, we discuss how zero-inflation influences parameter estimation. Finally, we compare the PN model to a model using two separate but correlated random effects. In simulation studies we find there is little advantage to the more complicated model.