Hyper Prior Dirichlet Partial Multinomial Logistic Regression Through Multiple Binary Responses for Mozambique HIV/AIDS

• Activity Number: 238 - SPEED: Environment and Health, Governmental Policies and Population Surveys, Part 1
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Diana Gonzalez* and Di Fang
• Companies: Arizona State University and University of Arkansas
• Keywords: prior; multinomial; logistic regression; clustered data; longitudinal data; MCMC

Abstract

Information was obtained from residents of Mozambique who were surveyed on simultaneous responses to blood test, heard of AIDS campaign, and heard of HIV.  We fit a hyper prior multinomial logistic regression model to jointly model these responses. This model analyzes the responses as a restricted multinomial obtained on blood test results, heard of AIDS campaign, and heard of HIV as opposed to those who had negative test and were oblivious to HIV. We used data obtained from households nested within clusters and clusters nested within counties in Mozambique. We made use of three priors. One prior, a Dirichlet prior on the multinomial probabilities from three binary responses to address household differences was instituted. One prior to account for the differences in probabilities within households, another across clusters and a third prior to address differences among the probabilities across counties. Inference is based on Markov chain Monte Carlo methods used to perform the computations. Our results outlined the benefits for such a model.