A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model

Abstract

This paper expands on a recent study by Muthen & Kaplan (1985) by examining the impact of non-normal Likert variables on testing and estimation in factor analysis for models of various size. Normal theory GLS and the recently developed ADF estimator are compared for six cases of non-normality, two sample sizes, and four models of increasing size in a Monte Carlo framework with a large number of replications. Results show that GLS and ADF chi-square tests are increasingly sensitive to non-normality when the size of the model increases. No parameter estimate bias was observed for GLS and only slight parameter bias was found for ADF. A downward bias in estimated standard errors was found for GLS which remains constant across model size. For ADF, a downward bias in estimated standard errors was also found which became increasingly worse with the size of the model.