Bayesian Inference for the Relationship Between Two Categorical Variables with Covariates for Clustered Data

• Activity Number: 339 - Official Statistics and Small Area Estimation
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Dilli Bhatta*
• Companies: University of South Carolina Upstate
• Keywords: Bayesian; Categorical data; Independence; multi-level logistic regression; Coavriates; TIMSS

Abstract

Analysis of categorical data, presented in a two-way contingency table, is a well known statistical problem in many real life applications. With such data, we make an inference about the possible association between two cross-classified categorical variables. Usually, the data presented in a two-way table are obtained from a simple random sampling (SRS), where the responses of the individuals are assumed to be independent of each other. In this paper, we consider cluster sample (type of complex sample survey data) and provide a test of independence between two categorical variables by incorporating PSU and SSU related covariates. It is likely that these covariates can be associated with two cross-classified categorical variables and thus may have impact on their association. We incorporate covariates via a multi-level logistic regression model and propose a two-stage Bayesian procedure in order to make an inference about association. We apply our methodology to the TIMSS data.