MULTI-GROUP ANALYSIS IN PLS-SEM: A STATISTICAL EXAMINATION OF MEASUREMENT INVARIANCE TECHNIQUES

Abstract

The measurement invariance is a key principle or concept in multi-group analysis (MGA) of structural equation model (SEM) and can be used to prove that a hypothesis is not viable or valid across numerous groups and thus, statistically weak. As the Partial Least Squares Structural Equation Modeling (PLS-SEM) has gained popularity, the main procedure of determining invariance in Smart PLS has become the Measurement Invariance of Composite Models (MICOM). Nevertheless, the MICOM lacks the statistical soundness and stability needed to compare it with the conventional difference testing of chi-square in the use of covariance-based SEM (CB-SEM). The objective of this paper is to statistically compare MICOM to chi-square difference testing using a design, based on a structure with simulation and an empirical data set. They used simulated data generated in different scenarios sample size, type of distributions (normal and non-normal), and type of measurement models (reflective and formative) to test the performance of each of them. A real dataset was used to do further analysis to represent the applicative verification of the complications of the simulation. The results provide that MICOM operates more reliably under small-sample and non-normal data circumstances especially within formative constructs but the chi-square difference testing is ultrasensitive to misspecification and sample size inflation. Configural, compositional, and equality of means/variances, are three stages of the MICOM procedure, which offers a much less restrictive and statistically conservative way of comparing models nested within a model. This paper suggests a statistical decision tree based on simulation evidence that will help the researchers in identifying suitable MGA techniques based on types of constructs, number of samples and characteristics of the data. This helps to improve methodological rigidity within multi-group PLS-SEM applications, particularly in applications that involve formative indicator use or small databases.