Smooth Hazards with Multiple Time Scales. An Application to Transitions from Cohabitation to Marriage

Angela Carollo , Max Planck Institute for Demographic Research
Jutta Gampe, Max Planck Institute for Demographic Research
Hein Putter, Leiden University Medical Center
Paul Eilers, Erasmus Medical Centre, Rotterdam

Marriage is frequently preceded by a period of cohabitation. The transition rate from cohabitation to marriage can be considered over two time scales, the age of the individual (age-specific rates) or the duration of the cohabitation. Traditional approaches choose one time scale as the dominant one and model the other time scale as a, possibly time-varying, covariate. We propose an approach to model a hazard jointly over two time dimensions. The model assumes a smooth bivariate hazard function, and the function is estimated by two-dimensional $P$-splines. We use data from the German Family Panel (pairfam), and we demonstrate that considering the two time scales jointly provides additional insights about the transition from cohabitation to marriage.

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 Presented in Session 32. Methods for Fertility and Life Course Analysis. Session within the Project of Excellence of the Department of Statistical Sciences of Padova University.