A New Flexible Generalized Heterogeneous Data Model (GHDM) with an Application to Examine the Effect of High Density Neighborhood Living on Bicycling Frequency

There is growing interest in multivariate dependent outcome models that include a mixture of different kinds of discrete and continuous variables. This may be attributed to at least two reasons. The first is the ability to generate multivariate distributions through the use of relatively flexible copula-based methods and/or effective factorization techniques for the covariance matrices. The second is the development of computationally efficient ways to estimate models based on variational methods for Bayesian inference or maximum approximate composite marginal likelihood methods for frequentist inference. However, there are two important assumptions in earlier mixed data models: (i) marginal normality of unobserved factors that generate jointness among the main outcome variables of interest, and (ii) independence between the unobserved factors and the propensity equations underlying the main outcomes of interest.