The Power of Approximate Tests for the Regression Coefficients in a Gamma Regression Model

A gamma regression model which has wide application in life-testing and analysis of point processes is considered. Approximate statistical tests for the regression coefficients based on maximum likelihood and weighted least squares fits of the model are considered. The power and significance level properties of the tests are evaluated for a model with a single regressor variate when the underlying gamma distributions have the same shape parameter. The tests give good control over the actual significance levels for all values of the shape parameter. The test using the maximum likelihood estimators has much better power than the test using the weighted least squares estimators for small values of the shape parameter but the power differences are negligible when the shape parameter exceeds five.