Testing for the mixture hypothesis of Poisson regression models

This paper considers testing the mixture hypothesis of Poisson regression models using the likelihood ratio (LR) test.The main motivation of the mixture hypothesis is the unobserved heterogeneity.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.We derive its limiting distribution by assuming popular Poisson regression models in terms of a Gaussian process.Furthermore, we discuss how to obtain the asymptotic critical values of the LR test consistently.Finally, we implement various Monte Carlo experiments and compare its power with the specification test proposed by Lee (1986).The simulation shows that the LR test is more powerful than the specification test when its small sample size distortion is adjusted.