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Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models

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Abstract

When fitting a Gaussian mixture regression model to observed data, estimating a between-group contrast can be a practical issue. One can use the estimate to compare the effects of a particular covariate or a set of covariates across different subpopulations. By applying fiducial generalized pivotal quantities, a small-sample solution is proposed in this paper to obtain interval estimates of between-group contrasts. Specifically, a Markov chain Monte Carlo sampler, which takes the membership uncertainty of each individual into account, is designed to generate realizations from the target distributions for computing the required interval estimates. A plant virus transmission study is first introduced as a motivating example for the present study. Next, the observed data are analyzed to illustrate the proposed method. Based on the simulation results, it is further shown that the proposed method can maintain the empirical coverage rates sufficiently close to the nominal level.

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Acknowledgements

I would like to thank the editor, an associate editor and two anonymous referees for their insightful comments and constructive suggestions. I am also grateful to Computer and Information Networking Center, National Taiwan University for the support of high-performance computing facilities. Shin-Fu Tsai’s research is supported in part by Ministry of Science and Technology, Taiwan (Grant No. MOST 107-2118-M-002-002-MY2).

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Authors and Affiliations

  1. Department of Agronomy, National Taiwan University, Taipei, 10617, Taiwan

    Shin-Fu Tsai

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  1. Shin-Fu Tsai
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Correspondence to Shin-Fu Tsai.

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Appendix: Simulation Results

Appendix: Simulation Results

See Tables 4, 5, 6, 7, 8 and 9.

Table 4 Empirical coverage rates of 90% confidence intervals.
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Table 5 Empirical coverage rates of 95% confidence intervals.
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Table 6 Empirical coverage rates of 99% confidence intervals.
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Table 7 Average width of 90% confidence intervals.
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Table 8 Average width of 95% confidence intervals.
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Table 9 Average width of 99% confidence intervals.
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Tsai, SF. Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models. JABES 24, 610–633 (2019). https://doi.org/10.1007/s13253-019-00364-4

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  • DOI: https://doi.org/10.1007/s13253-019-00364-4

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