Sample Size Requirements for Structural Equation Models

TLDR

Determining sample size requirements for structural equation modeling (SEM) is a challenge faced by investigators, reviewers, and grant writers, especially as the use of SEM has surged in behavioral science but often relies on outdated rules‑of‑thumb. The study evaluates sample size requirements for common applied SEMs using Monte Carlo data simulation techniques. The authors varied key model properties—number of indicators and factors, factor loadings, path coefficients, and missing data—in Monte Carlo simulations to assess their impact on power, bias, and solution propriety. Results show sample size requirements ranging from 30 to 460 cases, reveal patterns linking model parameters to required size, and underscore the limitations of commonly cited rules‑of‑thumb, with lessons for determining SEM sample size discussed.

Abstract

Determining sample size requirements for structural equation modeling (SEM) is a challenge often faced by investigators, peer reviewers, and grant writers. Recent years have seen a large increase in SEMs in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb. This study used Monte Carlo data simulation techniques to evaluate sample size requirements for common applied SEMs. Across a series of simulations, we systematically varied key model properties, including number of indicators and factors, magnitude of factor loadings and path coefficients, and amount of missing data. We investigated how changes in these parameters affected sample size requirements with respect to statistical power, bias in the parameter estimates, and overall solution propriety. Results revealed a range of sample size requirements (i.e., from 30 to 460 cases), meaningful patterns of association between parameters and sample size, and highlight the limitations of commonly cited rules-of-thumb. The broad "lessons learned" for determining SEM sample size requirements are discussed.