A comparison of confirmatory factor analysis of binary data on the basis of tetrachoric correlations and of probability-based covariances: A simulation study

Abstract

Although tetrachoric correlations provide a theoretically well-founded basis for the investigation of binary data by means of confirmatory factor analysis according to the congeneric model, the outcome does not always meet the expectations. As expected from analyzing the procedure of computing tetrachoric correlations, the data must show a high quality for achieving good results. In a simulations study it was demonstrated that such a quality could be established by a very large sample size. Robust maximum likelihood estimation improved model-data fit but not the appropriateness of factor loadings. In contrast, probabilitybased covariances and probability-based correlations as input to confirmatory factor analysis yielded a good model-data fit in all sample sizes. Probabilitybased covariances in combination with the weighted congeneric model additionally performed best concerning the absence of dependency on item marginals in factor loadings whereas probability-based correlations did not. The results demonstrated that it is possible to find a link function that enables the use of probability-based covariances for the investigation of binary data.