Log-linear Causal Analysis of Cross-classified Categorical Data

Abstract

Although log-linear and log-multiplicative analysis of association between variables is useful, its major limitation has been a lack of association with causal analysis. The objective of this article is to introduce a causal analysis on the basis of an adjusted cross-classified frequency table having such counterfactual odds ratios between a treatment variable X and its dependent variable Y that would be realized if the effects of confounding covariates on the association between X and Y were eliminated. The author first clarifies that the attainment of statistical independence between X and the covariates is not sufficient, because the issue of collapsibility remains even under completely randomized treatment allocation, and then proposes a specific standardization method for covariate states to solve this issue. By assuming semiparametric regression models, the author then introduces a new method of retaining the causal effects of X on Y, and the possible dependence of those effects on the third variable, in adjusted two-way or three-way contingency tables. As a result, the author also introduces a method for applying semiparametric logit and multinomial logit regression models that do not specify the effects of the confounding covariates V on Y. The estimation of standard errors for applying log-linear and log-multiplicative association models for the data of adjusted contingency tables is also described.