Abstract
This chapter describes the use of graphical models to analyse categorical data. After defining the (conditional) independence graph, the core ingredients of graphical modelling, conditional independence and graphs, are reviewed. The Markov properties for undirected independence graphs are then presented. These properties facilitate the interpretation of the association structure displayed in the independence graph. Subsequently, three types of graphical models for categorical data are discussed: undirected graphical log-linear models, where all the variables are treated on an equal footing; directed graphical models, where the variables are assumed to be completely ordered; and graphical chain models, where the variables are partitioned into ordered blocks. A simple example is used to illustrate the ideas, and the chapter concludes with some suggestions for further reading.
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Smith, P.W.F. (2023). Graphical Models for Categorical Data. In: Kateri, M., Moustaki, I. (eds) Trends and Challenges in Categorical Data Analysis. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-31186-4_2
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