The Causal Effects for a Causal Loglinear Model

TL;DR

This paper introduces a causal theory for loglinear models that calculates causal effects using odds ratios and Pearl's framework, distinguishing between models with and without interaction effects, and analyzing three types of interactions.

Contribution

It presents a novel causal analysis method for loglinear models, including the calculation of effects and interactions, incorporating the cell effect as a new interaction type.

Findings

Calculates causal effects using odds ratios and Pearl's theory.

Differentiates effects in models with and without multiplicative interactions.

Introduces the cell effect as a new interaction effect.

Abstract

The analysis of the causality is important in many fields of research. I propose a causal theory to obtain the causal effects in a causal loglinear model. It calculates them using the odds ratio and Pearl's causal theory. The effects are calculated distinguishing between a simple mediation model (model without the multiplicative interaction effect) and a mediation model with the multiplicative interaction effect. In both models it is possible also to analyze the cell effect, which is a new interaction effect. Then in a causal loglinear model there are three interaction effects: multiplicative interaction effect, additive interaction effect and cell effect