Abstract
Starting from perfectly discriminating nonmonotone dichotomous items, a class of probabilistic models with or without response errors and with or without intrinsically unscalable respondents is described. All these models can be understood as simply restricted latent class analysis. Thus, the estimation and identifiability of the parameters (class sizes and item latent probabilities) as well as the chi-squared goodness-of-fit tests (Pearson and likelihood-ratio) are free of the problems. The applicability of the proposed variants of latent class models is demonstrated on real attitudinal data.
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This research was supported by the Kulturamt der Stadt Wien, Magistratsabteilung 7.
The author wishes to thank the editor, Ivo W. Molenaar, as well as Clifford C. Clogg and the anonymous reviewers for their valuable comments on the earlier drafts of this paper.
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Formann, A.K. Latent class models for nonmonotone dichotomous items. Psychometrika 53, 45–62 (1988). https://doi.org/10.1007/BF02294193
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DOI: https://doi.org/10.1007/BF02294193