A Comparison of Factor Rotation Methods for Dichotomous Data

Exploratory factor analysis (EFA) is frequently used in the social sciences and is a common component in many validity studies. A core aspect of EFA is the determination of which observed indicator variables are associated with which latent factors through the use of factor loadings. Loadings are initially extracted using an algorithm, such as maximum likelihood or weighted least squares, and then transformed - or rotated - to make them more interpretable. There are a number of rotational techniques available to the researcher making use of EFA. Prior work has discussed the advantages of a number of these criteria from a theoretical perspective, but few previous studies compare their performance across a broad range of conditions. This simulation study compared eight factor rotation criteria in terms of how well they were able to group dichotomous indicator variables correctly on the same factor, order the indicators by the magnitude of the factor loadings (identifying those indicators that were most strongly associated with the factors) and estimate the inter-factor correlations. Results reveal a mixed pattern of performance among the various rotations with the orthogonal Equamax consistently near the top in terms of correctly grouping and ordering indicator variables, and the orthogonal Facparsim performing well with more observed indicators. Advice regarding possible rotations to use for researchers conducting EFA with dichotomous indicators is provided.