Prof. Luis Miguel Grilo

University of Évora, Portugal



Title of the paper: Challenges in Estimating Structural Equation Models with Ordinal Variables


Abstract: Structural equation modeling (SEM) is widely used across various fields, including engineering, social sciences, and health research. Often, SEM is applied to data collected through questionnaires that use ordinal-scale responses, such as Likert-type items. The Maximum Likelihood (ML) estimator, a common method within the Covariance-Based SEM (CB-SEM) framework, is frequently used in such cases. However, ML assumes multivariate normality and typically requires large sample sizes, which may not be feasible in practice. To address these limitations, researchers have turned to robust ML variants and alternative estimators like Diagonally Weighted Least Squares (DWLS). DWLS leverages polychoric correlations and simplifies computations by using only the diagonal elements of the weight matrix. This approach enhances numerical stability and efficiency, especially with small to moderate sample sizes. Despite these advantages, DWLS is sensitive to model misspecification and can struggle with small samples. In some instances, the information matrix may not be invertible, or the covariance matrix may become non-positive definite, indicating possible issues with model identification. An alternative is the consistent Partial Least Squares (PLSc) estimator, part of the Variance-Based SEM (VB-SEM) family. While VB-SEM and CB-SEM differ in estimation philosophy and purpose, PLSc is particularly effective when latent variables are reflective. It does not assume normality, handles small samples well, and performs robustly with complex models. Although DWLS and PLSc belong to different SEM frameworks, the interpretation of their path coefficients—regarding direction, magnitude, and significance—is often comparable. Given this similarity, a comparative study using real-world case studies was conducted to evaluate the performance of DWLS and PLSc. The findings suggest that PLSc offers a practical alternative when DWLS fails to converge or produce a valid solution.

Bio: Prof. Luís M. Grilo has been working on statistical modeling and data analysis, with a special interest in Engineering, Social and behavioral sciences, and Health Sciences. He has contributed to projects focused on the analysis of clinical data and has applied Structural Equation Modeling (SEM) to investigate psychosocial risks experienced by employees within corporate environments. Specifically, these models have been developed to identify predictors of stress and burnout syndrome in both workers and college students, with the goal of improving mental health and wellbeing. He has also done scientific research in Distribution Theory: developing exact and near-exact distributions for some statistics used in Multivariate Analysis. He holds a Ph.D. in Mathematics and Statistics, being currently the Director of the Department of Mathematics at the University of Évora, Portugal. He has actively participated as a member of Scientific and Organizing Committees for various conferences and meetings in the fields of Mathematics and Statistics, contributing with over 130 conference presentations. His editorial experience includes serving as a special issue editor for Springer books, as well as for prominent journals such as JAS and RiS (Taylor & Francis group).




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