Latent class model diagnosis from a frequentist point of view.

*(English)*Zbl 1210.62032Summary: This is in response to E. S. Garrett and S. L. Zeger [Biometrics 56, No. 4, 1055–1067 (2000; Zbl 1116.62428)] who, within the Bayesian framework, developed mainly graphical methods for latent class model diagnosis. Possible problems with this approach, and with its application to both generated and empirical data, are pointed out. The impact of the proposed tools cannot be understood by their reader, as no comparisons are made to results obtainable using established methods for latent class model diagnosis; this applies especially to overall goodness-of-fit tests, for which alternatives (bootstrap, Rudas-Clogg-Lindsay index of fit) are mentioned. Further, in one case of generated data, the methods proposed by Garrett and Zeger seem to give problematic results as to identifiability; in the case of the empirical data on major depression, they lead to accepting a suboptimal three-class model. In the latter case, one can be rather sure that an identifiable, well-fitting latent class model could have been identified, if Garrett and Zeger had also considered restricted latent class models.

##### Keywords:

goodness of fit; identifiability; model diagnosis; parametric bootstrap; restricted latent class models
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