Bayesian Factor Analysis for Clustered Categorical Data

• Activity Number: 347
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Taiyeong Lee*+ and Yongdai Kim
• Companies: SAS Institute Inc. and Seoul National University
• Keywords: Bayesian Factor Analysis ; MCMC algorithm ; Market Basket Analysis ; Factor Model

Abstract

We propose a Bayesian factor model for clustered binary data, which can be used for market basket analysis where each cluster corresponds to each customer, and binary vectors in each cluster represent the shopping history of the corresponding customer. We use latent variables for modeling dependency of binary vectors. That is, a vector of binary random variables is obtained by making the threshold of a vector of latent variables, which are assumed to be Gaussian random variables, at 0. Then we construct a factor model of latent variables. The proposed model is characterized by that each cluster has its own factor model, but the parameters can be shared across the clusters in the model. An efficient MCMC algorithm is developed and the method is illustrated on a real data set of market basket analysis