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      Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models

      Journal of Memory and Language
      Elsevier BV

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          Abstract

          This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forced-choice variables, question-answer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arcsine-square-root transformation to proportional data, ANOVA can yield spurious results. I discuss conceptual issues underlying these problems and alternatives provided by modern statistics. Specifically, I introduce ordinary logit models (i.e. logistic regression), which are well-suited to analyze categorical data and offer many advantages over ANOVA. Unfortunately, ordinary logit models do not include random effect modeling. To address this issue, I describe mixed logit models (Generalized Linear Mixed Models for binomially distributed outcomes, Breslow & Clayton, 1993), which combine the advantages of ordinary logit models with the ability to account for random subject and item effects in one step of analysis. Throughout the paper, I use a psycholinguistic data set to compare the different statistical methods.

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          Most cited references21

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          Mixed-effects modeling with crossed random effects for subjects and items

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            Approximate Inference in Generalized Linear Mixed Models

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              Nonlinear mixed effects models for repeated measures data.

              We propose a general, nonlinear mixed effects model for repeated measures data and define estimators for its parameters. The proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood (or restricted maximum likelihood) estimators for linear mixed effects models. We implement Newton-Raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models. Two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed.
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                Author and article information

                Journal
                Journal of Memory and Language
                Journal of Memory and Language
                Elsevier BV
                0749596X
                November 2008
                November 2008
                : 59
                : 4
                : 434-446
                Article
                10.1016/j.jml.2007.11.007
                2613284
                19884961
                f6fb2a98-bf2d-4e0b-9d9d-2b73a5c79ffb
                © 2008

                https://www.elsevier.com/tdm/userlicense/1.0/

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