BOOTSTRAPPING WITH SMALL SAMPLES IN STRUCTURAL EQUATION MODELING: GOODNESS OF FIT AND CONFIDENCE INTERVALS

Abstract

Structural equation modeling (SEM) has become a regular staple of social science research, however very little is known about small sample size use. A sample size of 200 or larger for SEM models has been advocated (Boomsma, 1983; Kline, 2011) and the main test of model fit (χ2 goodness-of-fit) is sample size dependent and performs optimally in a range of at least 200-400 (Kenny, 2012). Model complexity in SEM can vary, however, a simple model could hold potential benefits to a researcher without the ability to attain 200 observations. Thus research with models with less than 200 need to be considered more. Two manuscripts are presented, both stemming from a 3 x3 factorial simulation with varied sample sizes (n = 50, 100, 200), factor loadings (λ = 0.60, 0.75, 0.90), and bootstrap samples to the sample size n and a population sample of size N = 400. One study looks at SEM fit indices and independence from the χ2 test as well as bootstrap extension potential. The second study analyzed the use and ease of bootstrap confidence intervals (CIs) for any of the fit indices used in tradition SEM publications, a much needed addition to the field.