On the goodness-of-fit tests for gamma generalized linear models

An omitted covariate in the regression function leads to hidden or unobserved heterogeneity in generalized linear models (GLMs). Using this fact, we develop two novel goodness-of-fit tests for gamma GLMs. The first is a score test to check the existence of hidden heterogeneity and the second is a Hausman-type specification test to detect the difference between two estimators for the dispersion parameter. In addition to these developments, we reveal the undesirable behavior of the deviance test for gamma GLMs, which is still used by many scholars in practice. Exploiting real-world data, we demonstrate the application of our proposed method.