The Constant Shape Parameter Assumption in Weibull Regression

The usual assumption in Weibull regression is that the scale parameter is a function of the predictor variables, and the shape parameter is constant. We consider the problem of estimating parameters in the presence of a nonconstant shape parameter and the effect of assuming a constant shape parameter when it really is not constant. We consider both classical and Bayesian methods of estimation. The misspecification of a constant shape parameter can lead to a loss of power for tests regarding the slope parameters. We find that prediction intervals can be inaccurate when the shape parameter is incorrectly assumed to be constant.