This paper proposed the use of mutual information (MI) decomposition as a novel approach to identifying indispensable variables and their interactions for contingency table analysis. The MI analysis identified subsets of associative variables based on multinomial distributions and validated parsimonious log-linear and logistic models. The proposed approach was assessed using two real-world datasets dealing with ischemic stroke (with 6 risk factors) and banking credit (with 21 discrete attributes in a sparse table). This paper also provided an empirical comparison of MI analysis versus two state-of-the-art methods in terms of variable and model selections. The proposed MI analysis scheme can be used in the construction of parsimonious log-linear and logistic models with a concise interpretation of discrete multivariate data.