Direction of effects in categorical variables: Looking inside the table.

Abstract

In the variable-oriented domain, direction of dependence analysis of metric variables is defined in terms of changes that the independent (or causal) variable has on the univariate distribution of the dependent variable. In this article, we take a person-oriented perspective and extend this approach in two aspects, for categorical variables. First, instead of looking at univariate frequency distributions, direction dependence is defined in terms of special interactions. That is, direction dependence is defined as a process that can be detected "inside the table" instead of in its marginals. Second, the present approach takes an event-based perspective. That is, direction of effect is defined for individual categories of variables instead of the entire range of possible scores (or categories). Log-linear models are presented that allow researchers to test the corresponding hypotheses. Simulation studies illustrate characteristics and performance of these models. An empirical example investigates whether there is truth to the adage that money does not buy happiness. Extensions and limitations are discussed.