  In this paper we investigate the use of staged tree models for discrete
longitudinal data. Staged trees are a type of probabilistic graphical model for
finite sample space processes. They are a natural fit for longitudinal data
because a temporal ordering is often implicitly assumed and standard methods
can be used for model selection and probability estimation. However, model
selection methods perform poorly when the sample size is small relative to the
size of the graph and model interpretation is tricky with larger graphs. This
is exacerbated by longitudinal data which is characterised by repeated
observations. To address these issues we propose two approaches: the
longitudinal staged tree with Markov assumptions which makes some initial
conditional independence assumptions represented by a directed acyclic graph
and marginal longitudinal staged trees which model certain margins of the data.
