Nonlinear discrete-time hazard models for entry into marriage

When modeling the hazard of entry into marriage, the non-monotonic dependence on age needs to be taken into account. In this paper, nonlinear discrete-time hazard models based on a bell-shaped function are proposed, in which the support of the hazard function, the maximum hazard and the age of maximum hazard are estimated. Starting in the proportional hazards framework, the baseline hazard model proposed by Blossfeld and Huinink (1991) is extended to allow estimation of the support of the baseline hazard. A naive extension is shown to suffer from partial aliasing and thus an alternative parameterization is proposed, in which the partial aliasing is reduced. This parameterization includes the maximum hazard and the age of maximum hazard as parameters. A non-proportional hazards model is then obtained by allowing the age of maximum hazard, as well as the maximum hazard itself, to depend on covariates. The usefulness of the proposed models is demonstrated through application to data from the Living in Ireland Surveys conducted between 1994 and 2001.