Simultaneous factor analysis of dichotomous variables in several groups

A new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals. The method makes it possible to compare factor loading pattern, factor variances and covariances, and factor means over groups. The method uses information from first and second order proportions and estimates the model by generalized least-squares. Hypotheses regarding different degrees of invariance over groups may be evaluated by a large-sample chi-square test.The research of the first author was supported partly by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog, and partly by the Swedish Research Council in the Humanistic and Social Sciences under project Analysis of Contingency Tables, project director Bengt Muthén.