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Testing for the Mixture Hypothesis of Poisson Regression Models

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  • Jin Seo Cho

    (Yonsei University)

Abstract

The current study investigates testing the mixture hypothesis of Poisson regression models using the likelihood ratio (LR) test. The motivation of the mixture hypothesis stems from the unobserved heterogeneity, and the null hypothesis of interest is that there is no unobserved heterogeneity in the data. Due to the nonstandard conditions described in the text, the LR test does not weakly converge to the standard chi-squared random variable under the null hypothesis. We derive its null limit distribution as a functional of the Hermite Gaussian process. Furthermore, we introduce a methodology to obtain the asymptotic critical values consistently. Finally, we conduct Monte Carlo experiments and compare the power of the LR test with the specification test developed by Lee (1986).

Suggested Citation

  • Jin Seo Cho, 2025. "Testing for the Mixture Hypothesis of Poisson Regression Models," Working papers 2025rwp-254, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2025rwp-254
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    More about this item

    Keywords

    Mixture of Poisson Regression Models; Likelihood Ratio Test; Asymptotic Null Distribution; Gaussian Process.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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