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Heywood cases are known from linear factor analysis literature as variableswith communalities larger than 1.00, and in present day factor models, theproblem also shows in negative residual variances. For binary data, ordinalfactor models can be applied with either delta parameterization or thetaparametrization. The former is more common than the latter and can yieldHeywood cases when limited information estimation is used. The same problemshows up as nonconvergence cases in theta parameterized factor models and asextremely large discriminations in item response theory (IRT) models. In thisstudy, we explain why the same problem appears in different forms depending onthe method of analysis. We first discuss this issue using equations and thenillustrate our conclusions using a small simulation study, where all threemethods, delta and theta parameterized ordinal factor models (with estimationbased on polychoric correlations) and an IRT model (with full informationestimation), are used to analyze the same datasets. We also compared theperformances of the WLS, WLSMV, and ULS estimators for the ordinal factormodels. Finally, we analyze real data with the same three approaches. Theresults of the simulation study and the analysis of real data confirm thetheoretical conclusions.

Heywood cases in unidimensional factor models and item response models for binary data