Journal of Data Science

We demonstrate how to test for conditional independence of two variables with categorical data using Poisson log-linear models. The size of the conditioning set of variables can vary from 0 (simple independence) up to many variables. We also provide a function in R for performing the test. Instead of calculating all possible tables with for loop we perform the test using the loglinear models and thus speeding up the process. Time comparison simulation studies are presented.

Abstract: This article considers hypothesis testing using Bayes factor in the context of categorical data models represented in two dimensional contingency tables. The study includes multinomial model for a general I × J table data. Other data characteristics such as low as well as polarized cell counts and size of the tables are also considered. The objective is to investigate the sensitivity of Bayes factor taking these features into account so as to understand the performance of non-informative priors itself. Consistency has been studied based on different types of data and using Dirichlet prior with eight different choices for multinomial model followed by a bootstrap simulation. Study has emphasized the reasonable choice of values for the parameters that normally represents the underlying physical phenomena, though partially vague in nature.