"... this paper reviews the issue of what sample size and sample power the researcher should have in the EFA, CFA, and SEM study. Statistical power is the estimation of the sample size that is appropriate for an analysis. In any study, four parameters related to power analysis are Alpha, Beta, statistical power and Effect size. They are prerequisites for a priori sample size determination. Scale development in general and Factor Analysis (EFA, CFA) and SEM are large sample size methods because sample affects precision and replicability of the results. However, the existing literature provides limited and sometimes conflicting guidance on this issue. Generally, for EFA the stronger the data, the smaller the sample can be for an accurate analysis. In CFA and SEM parameter estimates, chi-square tests and goodness of fit indices are equally sensitive to sample size. So the statistical power and precision of CFA/SEM parameter estimates are also influenced by sample size.".
In CFA and SEM, sample size depends on a number of features like study design (e.g. cross-sectional vs. longitudinal); the number of relationships among indicators; indicator reliability, the data scaling (e.g., categorical versus continuous) and the estimator type (e.g., ML, robust ML etc.), the missing data level and pattern and model complexity (Brown, 2015). Thus, determining sample size is approximated by power analysis (Brown, 2015; Kline, 2016; Byrne, 2012; Wang & Wang 2012). Also, minimum sample sizes are recommended to limit the non-convergence probability to have unbiased estimates or standard errors based on Monte Carlo simulations studies. Generally, CFA/SEM is a large-sample technique (Kline, 2016) but as a
rule, models having robust parameter estimates and variables with high reliability may require smaller samples (Tabachnick & Fidell, 2013). Additionally, the issue whether the sample size is adequate for achieving desired power for significance tests, overall model fit, and likelihood ratio tests for specific model/research circumstances is a different aspect considered during power analysis (Hancock & French, 2013; Lee, Cai, & MacCallum, 2012). How Chi-square statistic, RMSEA, and other fit indices perform on different sample sizes levels is another parameter to consider (Hu & Bentler, 1999). Then there is sufficient power is crucial for individual parameter tests like factor loadings (Newsom, 2018). A CFA/SEM rule of thumb is the ratio of cases to free parameters, or N:q is commonly used for minimum recommendations and 10:1 to 20:1 is a commonly suggested ratio (Schumacker & Lomax, 2015; Kline, 2016; Jackson, 2003). Anyhow, even suggestions based on simulation studies are only rough approximations, not equally applicable to all SEM studies. Simulation studies have the potential to study only a fraction of SEM research conditions at a time thus they are not easily generalized (Brown, 2015; Newsom, 2018).