Exploring the Sensitivity of Horn's Parallel Analysis to the Distributional Form of Random Data

Horn's parallel analysis (PA) is the method of consensus in the literature on empirical methods for deciding how many components/factors to retain. Different authors have proposed various implementations of PA. Horn's seminal 1965 article, a 1996 article by Thompson and Daniel, and a 2004 article by Hayton, Allen, and Scarpello all make assertions about the requisite distributional forms of the random data generated for use in PA. Readily available software is used to test whether the results of PA are sensitive to several distributional prescriptions in the literature regarding the rank, normality, mean, variance, and range of simulated data on a portion of the National Comorbidity Survey Replication (Pennell et al., 2004) by varying the distributions in each PA. The results of PA were found not to vary by distributional assumption. The conclusion is that PA may be reliably performed with the computationally simplest distributional assumptions about the simulated data.