Bivariate modelling of clustered continuous and ordered categorical outcomes.

Simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types. Here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution. The approach is then extended to allow for clustering of the bivariate outcomes. The model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome. This factorization suggests convenient parameter estimation using estimating equations. Foetal weight and malformation data from a developmental toxicity experiment illustrate the results.