JinSeo.Cho - Testing for the Mixture Htpothesis of Poisson Regression Models

<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).