Tests for Detecting Overdispersion in the Positive Poisson Regression Model
针对截断于零的正泊松回归模型，推导了检验过度离散的得分检验，并开发了改进小样本性质的校正检验，通过蒙特卡洛实验评估其表现，并应用于美国制造业罢工数据。
This article derives score tests for extra-Poisson variation in the positive or truncated-at-zero Poisson regression model against truncated-at-zero negative binomial family alternatives. It also develops size-corrected tests of overdispersion that are expected to improve their small-sample properties. Further, small-sample performance of the tests is investigated by means of Monte Carlo experiments. As an illustration, the proposed tests are applied to a model of strikes in U.S. manufacturing. The proposed tests have an interpretation as conditional moment tests and require only the positive Poisson model to be estimated. It is shown that most of the tests for overdispersion in the regular Poisson model given in the econometric and statistical literature can be obtained as special cases of the tests developed in this article. Monte Carlo experiments indicate that the size correction, based on the asymptotic expansions of the score function, is effective in improving the accuracy of the size and power of the tests in small samples.