A mixture model for duration data: Analysis of second births in China.
When a given population is observed for only a limited period and an event such as the birth of a second child will not be experienced by everyone in that population, neither conventional binary response models nor regression models for duration data will correctly estimate the effects of covariates upon the probability or timing of the event. Boag in 1949 therefore proposed mixing a logistic regression model with a survival model in order to overcome the problem. The authors introduce a mixture model combining logistic regression and piecewise proportional hazards models for the analysis of duration data. The model allows the simultaneous estimation of both the probability and timing of an event. The model is illustrated through an analysis of the effects of women's characteristics and of the acceptance of a one-child certificate on the birth of second children in China. Both factors were found to affect the probability of having a second child, but only the acceptance of a one-child certificate has a significant and strong effect upon the second-birth interval.