Range Restriction Affects Factor Analysis: Normality, Estimation, Fit, Loadings, and Reliability.

Abstract

A sample suffers range restriction (RR) when its variance is reduced comparing with its population variance and, in turn, it fails representing such population. If the RR occurs over the latent factor, not directly over the observed variable, the researcher deals with an indirect RR, common when using convenience samples. This work explores how this problem affects different outputs of the factor analysis: multivariate normality (MVN), estimation process, goodness-of-fit, recovery of factor loadings, and reliability. In doing so, a Monte Carlo study was conducted. Data were generated following the linear selective sampling model, simulating tests varying their sample size ( $N$ = 200 and 500 cases), test size ( $J$ = 6, 12, 18, and 24 items), loading size ( $L$ = .50, .70, and .90), and restriction size (from $R$ = 1, .90, .80, and so on till .10 selection ratio). Our results systematically suggest that an interaction between decreasing the loading size and increasing the restriction size affects the MVN assessment, obstructs the estimation process, and leads to an underestimation of the factor loadings and reliability. However, most of the MVN tests and most of the fit indices employed were nonsensitive to the RR problem. We provide some recommendations to applied researchers.