Clusterwise multivariate regression of mixed-type panel data

Multivariate panel data of mixed type are routinely collected in many different areas of application, often jointly with additional covariates which complicate the statistical analysis. Moreover, it is often of interest to identify unknown groups of subjects in a study population using such data structure, i.e., to perform clustering. In the Bayesian framework, we propose a finite mixture of multivariate generalised linear mixed effects regression models to cluster numeric, binary, ordinal and categorical panel outcomes jointly. The specification of suitable priors on the model parameters allows for convenient posterior inference based on Markov chain Monte Carlo (MCMC) sampling with data augmentation. This approach allows to classify subjects in the data and new subjects as well as to characterise the cluster-specific models. Model estimation and selection of the number of data clusters are simultaneously performed when approximating the posterior for a single model using MCMC sampling without resorting to multiple model estimations. The performance of the proposed methodology is evaluated in a simulation study. Its application is illustrated on two data sets, one from a longitudinal patient study to infer prognosis groups, and a second one from the Czech part of the EU-SILC survey where households are annually interviewed to obtain insights into changes in their financial capability.