A three-level model for binary time-series data: the effects of air pollution on school absences in the Southern California Children's Health Study

A three-level model is proposed to simultaneously examine the effects of daily exposure to air pollution and individual risk factors on health outcomes without aggregating over subjects or time. We used a logistic transition model with random effects to take into account heterogeneity and overdispersion of the observations. A distributed lag structure for pollution has been included, assuming that the event on day t for a subject depends on the levels of air pollution for several preceding days. We illustrate this proposed model via detailed analysis of the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.