Efficient Bayesian analysis of multivariate aggregate choices

Abstract

In estimating individual choice behaviour using multivariate aggregate choice data, the method of data augmentation requires the imputation of individual choices given their partial sums. This article proposes and develops an efficient procedure of simulating multivariate individual choices given their aggregate sums, capitalizing on a sequence of auxiliary distributions. In this framework, a joint distribution of multiple binary vectors given their sums is approximated as a sequence of conditional Bernoulli distributions. The proposed approach is evaluated through a simulation study and is applied to a political science study.

Keywords:

• conditional Bernoulli
• data augmentation
• fixed-margin binary table
• Markov chain Monte Carlo
• multinomial logit

AMS Subject Classification:

• Primary: 62F15
• Secondary: 62P25

Acknowledgments

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0011866).