On testing the hidden heterogeneity in negative binomial regression models

초록

Negative binomial regression models have been widely used for analyzing overdispersed count data. However, when an important covariate is not included or individuals show some heterogeneity, negative binomial regression models may lead to erroneous standard errors or confidence intervals for the regression parameters. To test the existence of the hidden heterogeneity in negative binomial regression models, score statistics are developed under additive and multiplicative random effect models. We provide the explicit form of the score test statistics and their asymptotic distribution, and investigate the relationship between the score test statistics from the two random effect models. Our numerical study shows that the proposed score statistic has superior performance than existing methods in terms of controlling for the type I error and power.

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