  The problem we consider considers estimating a multivariate longitudinal
panel data model whose outcomes can be a combination of discrete and continuous
variables. This problem is challenging because the likelihood is usually
analytically intractable. Our article makes both a methodological contribution
and also a substantive contribution to the application. The methodological
contribution is to introduce into the panel data literature a particle
Metropolis within Gibbs method to carry out Bayesian inference, using a
Hamiltonian Monte Carlo (Neal 2011} proposal for sampling the vector of unknown
parameters. We note that in panel data models the Our second contribution is to
apply our method to carry out a serious analysis of the impact of serious life
events on mental health and excessive alcohol consumption. The dependence
between these two outcomes may be more pronounced when consumption of alcohol
is excessive and mental health poor, which in turn has implications for how
life events impact the joint distribution of the outcomes.
