An applied comparison of methods for least-squares factor analysis of dichotomous variables

Abstract

A statistical simulation was performed to compare four least-squares methods of factor analysis on datasets comprising dichotomous variables. Input matrices were: (1) phi correlation coefficients between the observed variables, (2) tetrachoric correlations estimated from bivariate tables of the observed variables, (3) tetrachoric correlations estimated on the basis of the latent continuous normal response variables underlying the observed variables (using LISCOMP with a weighted leastsquares factor extraction), or (4) correlations between the latent response variables underlying the observed variables based on a variant of latent trait theory (using NOHARM). The simulations were studied under varying sample sizes, threshold values, and population loadings of a factor model. Factor extraction was performed, and a measure of deviation between the population and estimated factor loadings was used as an index of fit. The more sophisticated and less readily available third and fourth methods were not found to be markedly superior to the first two methods, even for highly skewed data with small sample sizes. Further simulations were performed to demonstrate the stability of the results. Index terms: binary factor analysis, LISCOMP, NOHARM, simulation.