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On the Efficiency of Score Tests for Homogeneity in Two-Component Parametric Models for Discrete Data

Authors

  • David Todem,

    Corresponding author
    1. Department of Epidemiology and Biostatistics, Michigan State University, B601 West Fee Hall, East Lansing, Michigan 48824, U.S.A.
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  • Wei-Wen Hsu,

    1. Department of Statistics and Probability, Michigan State University, A413 Wells Hall East Lansing, Michigan 48824, U.S.A.
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  • KyungMann Kim

    1. Departments of Statistics and Biostatistics & Medical Informatics, University of Wisconsin-Madison, 600 Highland Ave., Madison, Wisconsin 53792, U.S.A.
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email: todem@msu.edu

Abstract

Summary In many applications of two-component mixture models for discrete data such as zero-inflated models, it is often of interest to conduct inferences for the mixing weights. Score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose. But the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model. In this article, we develop a score test of homogeneity that overcomes the limitations of existing procedures. The technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation. We exploit this decomposition to lay the foundation of the test. Simulation results show that the proposed covariate-adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights. A real-life example in dental caries research is used to illustrate the methodology.

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