Faster estimation of a discrete-time proportional hazards model with gamma frailty

Fitting a complementary log–log model that accounts for gamma-distributed unobserved heterogeneity often takes a significant amount of time. This is in part because numerical derivatives are used to approximate the gradient vector and Hessian matrix. The main contribution of this article is the use of Mata and a gf2 evaluator to express the gradient vector and Hessian matrix. Gradient vector expression allows one to use a few different options and postestimation commands. Furthermore, expression of the gradient vector and Hessian matrix increases the speed at which a likelihood function is maximized.