Value-Added Modeling

Hazard rate models are widely used to model duration data in a wide range of disciplines, from bio-statistics to economics. The aim of this insert is to supplement the portfolio of duration data analysis tools which Stata provides. pgmhaz estimates, by maximum likelihood, two discrete time (grouped duration data) proportional hazards regression models, one of which incorporates a gamma mixture distribution to summarize unobserved individual heterogeneity (or ‘frailty’). Covariates may include regressor variables summarizing observed differences between persons (either fixed or time-varying), and variables summarizing the duration dependence of the hazard rate. With suitable definition of covariates, models with a fully non-parametric specification for duration dependence may be estimated; so too may parametric specifications. pgmhaz thus provides a useful complement to cox and st stcox, weibull and st stweib. The two models estimated are: (1) the Prentice-Gloeckler (1978) model; and (2) the Prentice-Gloeckler (1978) model incorporating a gamma mixture distribution to summarize unobserved individual heterogeneity, as proposed by Meyer (1990). These are referred to as Model 1 and Model 2 respectively below. The versions of the Prentice-Gloeckler-Meyer hazard models estimated are as described by Stewart (1996), and my exposition of the models draws heavily on his paper