MEDIATION IN LOG-LINEAR MODEL

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 the concepts proposed by Pearl's causal theory where it is possible. My analysis can be divided into 2 parts. In the first part the effects are calculated distinguishing between a simple mediation model with 1 mediator (model without the multiplicative interaction effect between exogenous variable and mediator) and a mediation model with 1 mediator and the multiplicative interaction effect between exogenous variable and mediator. 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. In the second part the effects are calculated distinguishing between a mediation model with 2 parallel uncorrelated mediators and a mediation model with 2 parallel correlated mediators. In parallel mediation model with correlated influencing variables, Pearl?s theory cannot be used (Pearl, 2014) and and no alternative theory has been proposed. For this reason I propose a new causal concept with relatively formulas to calculate the causal effects in a mediation model with 2 parallel correlated mediators. These types of models are many important in marketing field: for example in customer satisfaction it is important to analyze a model where quality influences the positive and negative emotions and these 3 variables influence the future behavior. Then I show some applications of my causal theory to understand marketing problems.