Comparing Latent Structures of the Grade of Membership,Rasch, and Latent Class Models |
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Authors: | Email author" target="_blank">Elena?A?EroshevaEmail author |
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Institution: | (1) University of Washington, Box 354322, Seattle, WA 98195-4322, USA |
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Abstract: | This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using
the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds
generated by letting subject specific parameters vary over their natural range, while keeping other population parameters
fixed, in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities).
The case of a 2 × 2 contingency table is discussed in detail, and a generalization to 2J tables with J ≥ 3 is sketched. Our approach highlights the main distinction between the GoM model and the probabilistic mixture of classes
by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships. By using the
geometric approach we show that, in special cases, the GoM model can be thought of as being similar to an item response theory
(IRT) model in representing population heterogeneity. Finally, we show that the GoM item parameters can provide quantities
analogous to more general logistic IRT item parameters. As a latent structure model, the GoM model might be considered a useful
alternative for a data analysis when both classes of extreme responses, and additional heterogeneity that cannot be captured
by those latent classes, are expected in the population.
This work was supported by Award #1R03 AG18986-01 from the National Institute on Aging and NIH grant #1R01 CA94212-01. The
presentation of the ideas in this paper owes much to discussions with Stephen Fienberg and Brian Junker, Carnegie Mellon University.
The author thanks Jim Ramsay and two anonymous reviewers for their valuable comments on earlier drafts of this paper. |
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Keywords: | 2×2 contingency table fuzzy sets model geometric approach heterogeneity local independence |
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