2015Wiley StatsRef: Statistics Reference OnlineRequires access

Categorical Data, Marginal Models for

Geert Molenberghs

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Abstract

Abstract We briefly review two building blocks (generalized linear models and linear mixed models) for models for repeated categorical data. Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random‐effects models. A number of marginal models are presented for binary and ordinal data in turn. Major differences between marginal models and conditional models (such as loglinear models) are discussed. Attention is given to nonlikelihood‐based methods, such as generalized estimating equations and pseudo‐likelihood. We discuss marginal models that are derived from random‐effects specifications as well and place some emphasis on how to allow for overdispersion.

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What this paper is about

Abstract We briefly review two building blocks (generalized linear models and linear mixed models) for models for repeated categorical data. Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random‐effects models. A number of marginal models are presented for binary and ordinal data in turn. Major differences between marginal models and conditional models (such as loglinear models) are discussed. Attention is given to nonlikelihood‐based methods, such as generalized estimating equations and pseudo‐likelihood. We discuss marginal models that are derived from random‐effects specifications as well and place some emphasis on how to allow for overdispersion.

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Available abstract

Abstract We briefly review two building blocks (generalized linear models and linear mixed models) for models for repeated categorical data. Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random‐effects models. A number of marginal models are presented for binary and ordinal data in turn. Major differences between marginal models and conditional models (such as loglinear models) are discussed. Attention is given to nonlikelihood‐based methods, such as generalized estimating equations and pseudo‐likelihood. We discuss marginal models that are derived from random‐effects specifications as well and place some emphasis on how to allow for overdispersion.

Key concepts: Categorical variable, Marginal model, Overdispersion, Log-linear model, Quasi-likelihood, Generalized linear model, Generalized linear mixed model, Mathematics

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