In this chapter, we present an alternative modeling strategy to the fully parametric methods discussed in the previous chapter. Specifically, we consider the Cox proportional hazards model (Cox 1972, 1975). The Cox model is an attractive alternative to fully parametric methods because the particular distributional form of the duration times is left unspecified, although estimates of the baseline hazard and baseline survivor functions can be retrieved.

Problems with Parameterizing the Baseline Hazard

The parametric models discussed in Chapter 3 are desirable if one has a good reason to expect the duration dependency to exhibit some particular form. With the exception of the restrictive exponential model, any of the distribution functions discussed in the previous chapter are “flexible” inasmuch as the hazard rate may assume a wide variety of shapes, given the constraints of the model, i.e., the Weibull or Gompertz must yield monotonic hazards. However, most theories and hypotheses of behavior are less focused on the notion of time-dependency, and more focused on the relationship between some outcome (the dependent variable) and covariates of theoretical interest. In our view, most research questions in social science should be chiefly concerned with getting the appropriate theoretical relationship “right” and less concerned with the specific form of the duration dependency, which can be sensitive to the form of the posited model.

Moreover, ascribing substantive interpretations to ancillary parameters (for example the p, σ, or γ terms) in fully parametric models can, in our view, be tenuous.