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Population Heterogeneity Representations of Log-linear, Latent Class, Rasch and Grade of Membership Models

Elena A. Erosheva

Abstract:

This paper employs a geometric approach for describing population heterogeneity representations of different discrete data models. The case of a 2 x 2 contingency table is considered in details. The paper provides geometric representations for log-linear, latent class, Grade of Membership and Rasch models in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The approach generalizes 2 x 2 case to higher dimensions, i.e., to 2 ^J tables with $J \ge 3$. A discussion of similarities and differences among the models is included.

Keywords: Geometric approach, 2 x 2 contingency table, Marginal probabilities, Cell probabilities, Local independence.

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