Bayesian method for Analyzing Nominal Measures with Missing Values Using the Multinomial Probit Models.

Music City Center 

Missing data is common in scientific studies, including medical research and public health studies. We propose efficient Bayesian methods to analyze categorical data with missing values using the multinomial probit (MNP) model. In particular, we develop a Markov Chain Monte Carlo (MCMC) sampling method based on non-identifiable multinomial probit models and compare its performance with that of identifiable multinomial probit (MNP) models. We conduct our investigation through simulation studies, which show that the proposed methods can handle substantial missing values. The method of marginalizing redundant parameters based on the non-identifiable model outperforms the others in terms of mixing and convergence of the MCMC sampling components. We then apply the proposed methods to Mental Health Client-Level Data (MH-CLD) collected by the State Mental Health Agency (SMHA).

missing data

categorical data

MCMC

multinomial probit 

Section on Bayesian Statistical Science