# Efficient Bayesian estimation for flexible panel models for multivariate outcomes: Impact of life events on mental health and excessive alcohol consumption

## TL;DR

This paper introduces a novel Bayesian estimation method using particle Metropolis within Gibbs and Hamiltonian Monte Carlo for complex multivariate panel data with mixed outcomes, applied to study life events' effects on mental health and alcohol use.

## Contribution

It develops a new Bayesian inference approach for multivariate panel models with mixed outcomes and applies it to analyze the impact of life events on health and behavior.

## Key findings

- Life events significantly affect mental health and alcohol consumption.
- Dependence between outcomes is stronger with poor mental health and excessive drinking.
- Method improves inference for complex panel data models.

## Abstract

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.