Small Sample Estimation of Structural Equation Models: A Comparison of Alternative Estimation Approaches

Graham G. Rifenbark, Yves Rosseel

DOI: 10.64028/bwdg391439

Keywords: structural equation models, two-stage estimation, structural-after-measurement, small sample size, parameter recovery

TL;DR: An investigation of alternative modeling approaches and estimation techniques compared to SEM with a focus on parameter recovery.

Abstract: Typically, structural equation model (SEM) parameters are estimated using maximum likelihood (ML) which possess desirable attributes related to point estimation and inferences; however, ML is a large sample estimation method. In practice, researchers are often confronted with small sample sizes. When ML is used in these settings a host of issues can surface, including model nonconvergence, improper solutions, biased point estimates, and poor inference quality. Ultimately, latent parameters (e.g., regressions) are of most interest and the accuracy of these estimates is paramount. Alternative modeling approaches such as factor score regression (FSR) and the structural-after-measurement framework (SAM, Rosseel \& Loh, 2024) have been proposed and can be useful in the context of small sample size. In lieu of traditional (unbounded) ML, bounded ML estimation is a viable alternative for SEM, FSR, and SAM; whereas, non-iterative estimation is feasible for two-stage approaches (e.g., SAM). Therefore, we executed a Monte Carlo simulation to compare the performance of SEM, FSR, and SAM in which we systematically varied sample size, construct reliability, number of measurement blocks, and estimation bound type. For the SAM approach, we evaluated two different estimation procedures at stage-1: a non-iterative estimation method (multiple group method) and ML; whereas, we used ML for both stages of estimation for FSR. Outcomes of interest included convergence rates and estimation accuracy of structural parameters. We report the results from this Monte Carlo simulation and discuss implications for research with limited sample sizes.

Submission Number: 22