The performance of unweighted least squares and regularized unweighted least squares in estimating factor loadings in structural equation modeling

Zulkifli, N.; Aimran, N.; Deni, S.

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International Journal of Data and Network Science

ISSN 2561-8156 (Online) - ISSN 2561-8148 (Print) Quarterly Publication Volume 7 Issue 3 pp. 1017-1024 , 2023

The performance of unweighted least squares and regularized unweighted least squares in estimating factor loadings in structural equation modeling Pages 1017-1024 Download PDF

Authors: Nurul Raudhah Zulkifli, Nazim Aimran, Sayang Mohd Deni

DOI: 10.5267/j.ijdns.2023.6.004

Keywords: Monte Carlo simulation, Regularization, Unweighted least square, Regularized unweighted least square

Abstract: In a confirmatory study, researchers are expected to employ the covariance-based structural equation modeling (CB-SEM). One of the key presumptions when utilizing CB-SEM is that the data is multivariate normal. Nevertheless, a perfect normal distribution is rarely observed in real-life data. To resolve this, the unweighted least square (ULS) is designed to specifically deal with non-normal data in SEM. However, ULS often yields improper solutions like negative, or boundary estimates of unique variances since it considers measurement errors in observed variables. The disturbance in SEM is reflected in unique variance, which is random error due to unreliability or measurement error and reliable variation in the item that indicates unknown latent causes. Consequently, this can generate bias in indicator loadings estimates. As an action to disentangle this issue, the present study proposes the implementation of regularization parameters by adding small positive values to the variance-covariance matrix. The ratio of bias to variance in a model can be improved to obtain the best estimation performance. Pro-Active Monte Carlo simulation was used to produce multivariate non-normal data with designated sample sizes and population characteristics. The data were analyzed using R Programming Environment by employing “psych”, “MASS”, “foreign”, “mvrnonnorm”, “purr”, and “semTools” packages with 1000 replications to produce multivariate non-normal data. Next, the “lavaan” package was used for SEM and regularized SEM analyses. The outcome of this study proves the capability of regularized ULS to improve parameter estimation.

How to cite this paper

 Zulkifli, N., Aimran, N & Deni, S. (2023). The performance of unweighted least squares and regularized unweighted least squares in estimating factor loadings in structural equation modeling.International Journal of Data and Network Science, 7(3), 1017-1024.

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