Investigating the application of generalized additive models to discrete-time event history analysis for birth events

BACKGROUND Discrete-time event history analysis (EHA) is the standard approach taken when modelling fertility histories collected in surveys, where the date of birth is often recorded imprecisely. This method is commonly used to investigate the factors associated with the time to a first or subsequent conception or birth. Although there is an emerging trend towards the smooth incorporation of continuous covariates in the broader literature, this is yet to be formally embraced in the context of birth events. OBJECTIVE We investigate the formal application of smooth methods implemented via generalized additive models (GAMs) to the analysis of fertility histories. We also determine whether and where GAMs offer a practical improvement over existing approaches. We fit parity-specific logistic GAMs to data from the UK Household Longitudinal Study, learning about the effects of age, period, time since last birth, educational qualification, and country of birth. First, we select the most parsimonious GAMs that fit the data sufficiently well. Then we compare them with corresponding models that use the existing methods of categorical, polynomial, and piecewise linear spline representations in terms of fit, complexity, and substantive insights gained.