A phase type model of cohabiting union

Jean-Marie Le Goff, Université de Lausanne

In our communication, we propose a phase-type model to analyze the duration of non-conjugal cohabiting unions. This model is a competing risks model with two events that can end a cohabiting union, the marriage with the partner or the separation. We suppose that a non-marital union can be characterized by two hidden phases. The first begins at the start of the union and at each moment, people have the possibility to move to the second phase from which hazard rates of marriage and of separation differ from the first phase. The phase-type model we develop consider that each hazard rate is constant across the time (markovian approach). Investigations made on data of the British 1958 national child study and the 1970 British national study show that the proposed model fits well with data about the first cohabiting union of interviewed people. They however show that processes of marriage and separation differed between the two cohorts.