Chain event graphs (CEGs) extend graphical models to address situations in which, after one variable takes a particular value, possible values of future variables differ from those following alternative values. These graphs are a useful framework for modelling discrete processes which exhibit strong asymmetric dependence structures, and are derived from probability trees by merging the vertices in the trees together whose associated conditional probabilities are the same.
We exploit this framework to develop new classes of models where missingness is influential and data are unlikely to be missing at random. Context-specific symmetries are captured by the CEG. As models can be scored efficiently and in closed form, standard Bayesian selection methods can be used to search over a range of models. The selected maximum a posteriori model can be easily read back to the client in a graphically transparent way.
The efficacy of our methods are illustrated using a longitudinal study from birth to age 25 of children in New Zealand, analysing their hospital admissions aged 18-25 years with respect to family functioning, education, and substance abuse aged 16-18 years. Of the initial 1265 people, 25% had missing data at age 16, and 20% had missing data on hospital admissions aged 18-25 years. More outcome data were missing for poorer scores on social factors. For example, 21% for mothers with no formal education compared to 13% for mothers with tertiary qualifications.
This is joint work with Lorna Barclay and Jim Smith.