Log-Linear Transformation of Binary Variables: A Suitable Input for SEM

Abstract

A great obstacle for wider use of structural equation modeling (SEM) has been the difficulty in handling categorical variables. Two data sets with known structure between 2 related binary outcomes and 4 independent binary variables were generated. Four SEM strategies and resulting apparent validity were tested: robust maximum likelihood (ML), tetrachoric correlation matrix input followed by SEM ML analysis, SEM ML estimation for the sum of squares and cross-products (SSCP) matrix input obtained by the log-linear model that treated all variables as dependent, and asymptotic distribution-free (ADF) SEM estimation. SEM based on the SSCP matrix obtained by the log-linear model and SEM using robust ML estimation correctly identified the structural relation between the variables. SEM using ADF added an extra parameter. SEM based on tetrachoric correlation input did not specify the data generating process correctly. Apparent validity was similar for all models presented. Data transformation used in log-linear modeling can serve as an input for SEM.