7 Sample size for structural equation modeling

7.1 Introduction

Structural equation modeling (SEM) is a large‐sample approach. It is widely recognized that small sample sizes can cause a series of problems, including, but not limited to, failure of estimation convergence, improper solutions (e.g. negative variance estimates, correlation estimates greater than 1.0 or less than −1.0), lowered accuracy of parameter estimates, small statistical power, and inappropriate model fit statistics. As in other statistical modeling, determination of appropriate sample size is critical to SEM.

This chapter introduces some fundamental concepts of sample size estimation and power analysis for SEM. Starting with descriptions of often‐used rules of thumb in Section 7.2, different methods for sample‐size estimation for SEM are presented in the following sections. Applications of the Satorra‐Saris method and Monte Carlo simulation to sample‐size estimation and power analysis for confirmatory factor analysis (CFA) and latent growth models are demonstrated in Sections 7.3 and 7.4, respectively. Section 7.5 presents applications of two methods – the MacCallum–Browne–Sugawara's method and Kim's method – for sample‐size estimation based on model fit statistics/indexes. Sample‐size estimation for mixture models is still a challenge. We demonstrate in Section 7.6 how to use the Dziak–Lanza–Tan's method to estimate sample size for unconditional latent class analysis (LCA) with dichotomous items. ...

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