Using split-population models to examine predictors of the probability and timing of parity progression

Survival models are widely used in demography to analyse the timing of events such as death or leaving school. However, for events such as marriage or childbirth that are not experienced by everyone, standard survival analysis conflates the speed of progressing to an event with the proportion that never experience the event. The problem can be overcome by applying a 'split population' or 'cure' survival time model which splits the population into those who eventually experience the event and those who do not, and determines the speed of progression for the former. This paper demonstrates the use of split-population models in examining variables which affect the propensity and timing of additional births. The data analysed are from a sample of women from the 2001 Household, Income and Labour Dynamics in Australia (HILDA) Survey (N = 4,611). We model the propensity and time to have another child given sex composition of existing children, number of siblings and age at first birth for three cohorts of women. The study finds evidence of a preference for a mixed-sex composition, and an increased propensity for women with two boys to try for a third child. Women in later cohorts tend to have more children if they themselves come from larger families. Age at first birth is strongly associated with the propensity to have another child and with the speed of progression.