A wide variety of models for duration data have been discussed. Each of the approaches has certain advantages and disadvantages. The principal argument we have made is that in most social science settings, the Cox model should generally be preferred over its alternatives, for example the parametric models or some of the discrete models discussed in the last chapter. In this chapter, we revisit some of the models proposed and discuss some of the desirable and undesirable features inherent in the implementation of them. Following this discussion, we consider another class of models that create, in a sense, a “middle ground” between the Cox and parametric alternatives. The basic models discussed in this section are proposed by Royston (2001) and Royston and Parmar (2002).

Advantages and Disadvantages of Modeling Strategies

In this section, we discuss some of the advantages and disadvantages of the parametric models, discrete-time models, and the Cox models. We consider the standard parametric models first.

Parametric Models Revisited

The principal advantage of parametric duration models is the ability of the model to provide parameter estimates while simultaneously producing a relatively simple and easy-to-interpret characterization of the baseline hazard rate. Further, the parametric approach is flexible insofar as one simply needs to specify one of any number of suitable distribution functions. Commonly (and often by default), the Weibull distribution function is the distribution of choice in many applications; but there are numerous other functions that can be applied to duration data (each having concomitant assumptions regarding h0(t)).