A log-logistic regression model for a transition rate with a starting threshold

The paper presents a new type of parametric transition rate model that is particularly suitable for studying household and union formation. In such studies, it is often not easy to determine the moment at which individuals actually enter the population at risk - or at least when the risk begins to become socially important. Even in the presence of regulations stipulated by law, one might be interested in studying ‘social’ timetables. We assume that there is a constant rate for any duration and that after a certain threshold point a log-logistic rate is added, with this threshold as its time origin. This can be justified in a behavioural sense by assuming that random and social transitions arise from separate processes. We then apply the model to union formation in Italy and show how threshold and intensity effects generated by theoretical hypotheses can be revealed.