A comparative study on the performance of maximum likelihood, generalized least square, scale-free least square, partial least square and consistent partial least square estimators in structural equation modeling

Raudhah Zulkifli,Fatin Najihah Badarisam,Sayang Mohd Deni,Nazim Aimran

doi:10.5267/j.ijdns.2021.12.015

Abstract

Structural equation modeling offers various estimation methods for estimating parameters. The most used method in covariance-based structural equation modeling (CB-SEM) is the maximum likelihood (ML) estimator. The ML estimator is typically used when fitting models with normally distributed data. The growth of partial least squares path modeling (PLS-PM), including consistent partial least squares (PLSc), has also been noticed by researchers in the SEM fields. The PLSc has elevated interest in the scholastic setting in measuring the performance of various estimation methods in structural equation modeling. The choice of estimation methods has substantial impact in yielding parameter estimates. There could be a trade-off among the estimation methods’ ability to deal with different types of data based on the model tested. Accordingly, this study aims to compare the performance of ML, generalized least squares (GLS), and scale-free least squares (SFLS) for CB-SEM as well as partial least squares (PLS) and consistent partial least squares (PLSc). Multivariate normal data were generated using Monte Carlo simulation with pre-determined population parameters and sample sizes using R Programming packages. To produce the estimated values, data analysis was performed using AMOS and SmartPLS for CB-SEM and PLS-SEM, respectively. The findings illustrate notable similarities between CB-SEM (ML) and PLS-SEM results when the true indicator loading is certainly high.

Highlights

The second-generation statistical analysis technique, structural equation modeling (SEM), is established for evaluating the inter-relationships among numerous variables in a model (Awang, 2015; Ainur et al, 2017)
While covariance-based structural equation modeling (CB-SEM) is generally developed for confirmatory research, variance-based SEM (VB-SEM) is known as a prediction-based approach to SEM that is mostly utilized for exploratory research (Sarstedt et al, 2014)
At sample size 50, where the items’ true indicator loading was set as 0.7, partial least squares (PLS) consists of only 1 low Comparative Bias Index (CBI) value and performs markedly better than PLSc and CB-SEM estimators

Summary

Introduction

The second-generation statistical analysis technique, structural equation modeling (SEM), is established for evaluating the inter-relationships among numerous variables in a model (Awang, 2015; Ainur et al, 2017). PLS-SEM has been widely used in most social science fields (Hair et al, 2018). The goal of CB-SEM is to estimate model parameters that minimize the discrepancies between the observed sample covariance matrix once the improved theoretical model has been validated (Awang, 2015). The normality of data distributions is necessary for several estimators in CB-SEM, which is rarely encountered in social sciences study. PLS-SEM, on the other hand, functions well with non-normal data and has very few limitations when it comes to the application of ordinal and binary scales (Hair et al, 2017)

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Conclusion