ABSTRACT
This chapter introduces multivariate models for various types of responses including continuous, proportion, counts, events, etc. It shows that general multivariate models can be generated by connecting DHGLMs for various responses with correlated random effects. The R package mdhglm was developed for fitting multivariate HGLMs, as well as multivariate DHGLMs. The main function in the R package mdhglm is jointfit(). Correlation between random components is essential in the definition of joint models, where correlations among multivariate responses are modeled via correlated random effects. Several longitudinal models can be linked together to compose a multivariate hierarchical generalized linear model. The Rheumatoid Arthritis Patients rePort Onset Re-activation sTudy is a longitudinal study that aims to identify an increase in disease activity by self-reported questionnaires. The mdhglm package is used to fit MDHGLMs in which multivariate responses may vary and follow the DHGLM. Fixed and random effects can also be fitted in both the mean and the dispersion components.
