Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety

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in the behavioral science literature, but consideration of sample size requirements for applied SEMs often relies on outdated rules-of-thumb.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.

Keywords: Monte Carlo simulation; bias; confirmatory factor analysis; sample size; solution propriety; statistical power; structural equation modeling.

Figure 1. Schematic diagram of CFA model permutations

Note. The figure shows a representation of the model characteristics that were varied in the Monte Carlo analyses of the CFAs. We evaluated models with one to three factors and each factor in the model was indicated by three to eight indicators, which loaded on their respective factors at .50, .65, or .80. The factor correlation(s) was set to r = .30 or .50. CFA = confirmatory factor analysis; mag = magnitude.

Figure 2. Schematic diagram of mediation model permutations

Note. The strength of all the direct regressive paths was varied from .25 to .40 to .50 to account for 16%, 45%, and 75% of the variance in the dependent variable, respectively. All variables were set to have a variance of 1.0 and mean of 0. Arrows pointing toward the dependent variable show the amount of residual variance in each variable.

Figure 3. Minimum sample size required for CFA, SEM, and missingness models

Note. Ind = indicator; CFA = confirmatory factor analysis. Panels A to E show the results of the Monte Carlo simulation studies. Each panel shows the minimum sample size required for each permutation of each type of model that was evaluated. For panel E, Model A is the CFA model and Model B is the SEM model. The permutations of the regressive model (i.e., mediation model) differed in both the magnitude of the structural parameters and the total variance explained in the dependent variable (as shown in parentheses).