Use of ULS-SEM and PLS-SEM to Measure a Group Effect in a Regression Model Relating Two Blocks of Binary Variables

Abstract

The objective of this paper is to describe the use of unweighted least squares (ULS) structural equation modeling (SEM) and partial least squares (PLS) path modeling in a regression model relating two blocks of binary variables, when a group effect can influence the relationship. Two sets of binary variables are available. The first set is defined by one block X of predictors and the second set by one block Y of responses. PLS regression could be used to relate the responses Y to the predictors X, taking into account the block structure. However, for multigroup data, this model cannot be used because the path coefficients can be different from one group to another. The relationship between Y and X is studied in the context of structural equation modeling. A group effect A can affect the measurement model (relating the manifest variables (MVs) to their latent variables (LVs)) and the structural equation model (relating the Y -LV to the X-LV). In this paper, we wish to study the impact of the group effect on the structural model only, supposing that there is no group effect on the measurement model. This approach has the main advantage of allowing a description of the group effect (main and interaction effects) at the LV level instead of the MV level. Then, an application of this methodology on the data of a questionnaire investigating sun exposure behavior is presented.