An Applied Comparison of Methods for Least- Squares Factor Analysis of Dichotomous Variables

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Abstract
A statistical simulation was performed to com pare four least-squares methods of factor analysis on datasets comprising dichotomous variables. In put matrices were: (1) phi correlation coefficients between the observed variables, (2) tetrachoric correlations estimated from bivariate tables of the observed variables, (3) tetrachoric correlations esti mated on the basis of the latent continuous nor mal response variables underlying the observed variables (using LISCOMP with a weighted least- squares factor extraction), or (4) correlations be tween 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 marked ly superior to the first two methods, even for high ly skewed data with small sample sizes. Further simulations were performed to demonstrate the sta bility of the results.

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