Log-Linear and Log-Multiplicative Association Models for Categorical Data

Carolyn Jane Anderson, Maria Kateri, Irini Moustaki

Research output: Chapter in Book/Report/Conference proceedingChapter


The chapter reviews uni- and multidimensional association models (AMs) that provide a parsimonious modelling of interactions between categorical variables. AMs go beyond the standard log-linear modeling framework to model non-saturated models that exist between a saturated and an independence model, including also log-nonlinear models. AMs are presented here both graphically and algebraically to aid interpretation and help in understanding the features and structures of the associations. The chapter discusses the connection of AMs with graphical models and item response theory (IRT) models developed in Psychometrics that open new insights in the understanding and modeling of associations of categorical variables. Estimation methods within the maximum likelihood estimation framework including composite likelihood methods, goodness-of-fit tests and measures, as well as R packages available, are discussed. The models are fitted to data from massively open online courses (MOOCs) using the R package logmulti and on the data from the depression, anxiety and stress scale (DASS) using the R package pleLMA.
Original languageEnglish (US)
Title of host publicationTrends and Challenges in Categorical Data Analysis
Subtitle of host publicationStatistical Modelling and Interpretation
EditorsMaria Kateri, Irini Moustaki
ISBN (Electronic)9783031311864
ISBN (Print)9783031311857, 9783031311888
StatePublished - Jul 2023

Publication series

NameStatistics for Social and Behavioral Sciences
ISSN (Print)2199-7357
ISSN (Electronic)2199-7365


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