Structural equation modeling (SEM) of categorical and mixed-data using the novel Gifi transformations and information complexity (ICOMP)

Abstract

This paper introduces and develops a novel and computationally feasible alternative approach to the analysis of categorical, dichotomous, and mixed data sets in structural equation models (SEMs) to overcome currently existing problems. Our approach is based on the Gifi system. The Gifi system uses the optimal scaling methodology to quantify the observed categorical variables. In the quantification process, information in the observed variable is retained in the quantified variable. That is, the Gifi system transforms categorical data to continuous data without destroying the scale properties of the categorical variables. The scaling is thus preserved in the transformed nonlinear continuous Gifi data space. Hence the transformation is invertible. This is one of the unique characteristics of the Gifi system which avoids the arbitrary thresholding specification that is currently practiced and used in the literature. After the Gifi transformation, we analyze the transformed data set using SEM based on the multinormal distributional assumption. Such an approach legitimizes the distributional assumption of multivariate normality in SEM. Information-theoretic model selection criteria such as Akaike's [1] AIC, Bozdogan's [2] Consistent AIC, called CAIC, and the information-theoretic measure of complexity ICOMP criterion of Bozdogan [3-7] are introduced and develop as measures of fit in SEMs. The model with the minimum values of the criteria is selected as the best fitting model among a portfolio of candidate models. We provide a real benchmark numerical example using SEM on a categorical data set which measures the quality of life (QOL) to illustrate the versatility and flexibility of our approach using the Gifi transformations on this data set and fit five alternative SEM models by scoring the model selection criteria.