ABSTRACT
Models with a time-dependent transition rate, as surveyed in chapter 7, are based on specific parametric assumptions about the distribution of durations and allow for straightforward maximum likelihood estimations. As demonstrated in detail, time in these models normally serves as a proxy variable for a latent causal factor that is difficult to measure directly. The problem in substantive applications is that theories in the social sciences, at least at their current level of development, rarely offer strong arguments for a specific parametric model. We therefore suggested in chapter 7 to use these models with extreme caution. Estimating a variety of model specifications and comparing the outcomes seems to be an appropriate strategy. However, this leads to another problemml: the adequacy of alternative parametric models of time-dependence can only be evaluated with heuristic tools, as demonstrated in chapter 8. Although these goodness-of-fit checks may provide some rough hints as to which classes of models may be preferable, they cannot serve as strict tests to support a specific parametric model. Therefore, an interesting alternative strategy is to specify only a functional form for the influence of covariates, but leave the shape of the transition rate as unspecified as possible. Such models are known as semi-parametric models.
