Data generation for composite-based structural equation modeling methods

Rainer Schlittgen,Christian M Ringle,Marko Sarstedt

doi:10.1007/s11634-020-00396-6

Abstract

Examining the efficacy of composite-based structural equation modeling (SEM) features prominently in research. However, studies analyzing the efficacy of corresponding estimators usually rely on factor model data. Thereby, they assess and analyze their performance on erroneous grounds (i.e., factor model data instead of composite model data). A potential reason for this malpractice lies in the lack of available composite model-based data generation procedures for prespecified model parameters in the structural model and the measurements models. Addressing this gap in research, we derive model formulations and present a composite model-based data generation approach. The findings will assist researchers in their composite-based SEM simulation studies.

Highlights

Research in the social sciences often involves inference about concepts such as attitudes, perceptions, and behavioral intentions
In factor-based Structural equation modeling (SEM) unobservable conceptual variables are approximated by common factors under the assumption that each latent variable exists as an entity independent of observed variables
Many methods fall into the domain of compositebased SEM, partial least squares (PLS; Lohmöller 1989; Wold 1982) and generalized structured component analysis (GSCA; Hwang and Takane 2004) constitute the most advanced and frequently used approaches in the field (Hwang et al 2020; Hwang and Takane 2014)

Summary

Introduction

Research in the social sciences often involves inference about concepts such as attitudes, perceptions, and behavioral intentions. The studies usually have evaluated composite-based SEM methods on the grounds of factor model data, where the indicator covariances define the nature of the data (Sarstedt et al 2016). These studies univocally show that composite-based SEM methods produce biased results that typically manifest themselves in measurement model parameters (i.e., indicator loadings and weights) being overestimated and structural model parameters being underestimated (Goodhue et al 2012; Lu et al 2011; Reinartz et al 2009) These results are not considering that the estimated models were misspecified with regard to the data generation process in the simulation studies—as noted by numerous authors (Marcoulides et al 2012; Rigdon 2012; Rigdon et al 2017).. The package cbsem (Schlittgen 2019) of the statistical software R (R Core Team 2019) contains all functions described in the further course of this article

The composite-based model

The covariance matrix of the composites

Computation

Example

Data generation

Conclusion