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Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models

Hui, Francis; Muller, Samuel; Welsh, Alan

Description

There has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear mixed models. In this article, motivated by the increasing number of applications of mixed...[Show more]

dc.contributor.authorHui, Francis
dc.contributor.authorMuller, Samuel
dc.contributor.authorWelsh, Alan
dc.date.accessioned2021-01-12T03:31:47Z
dc.date.available2021-01-12T03:31:47Z
dc.identifier.issn0306-7734
dc.identifier.urihttp://hdl.handle.net/1885/219291
dc.description.abstractThere has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear mixed models. In this article, motivated by the increasing number of applications of mixed models where interest is on the variance components, we study the effects of random effects misspecification on random effects inference in linear mixed models, for which there is considerably less literature. Our findings are surprising and contrary to general belief: for point estimation, maximum likelihood estimation of the variance components under misspecification is consistent, although in finite samples, both the bias and mean squared error can be substantial. For inference, we show through theory and simulation that under misspecification, standard likelihood ratio tests of truly non‐zero variance components can suffer from severely inflated type I errors, and confidence intervals for the variance components can exhibit considerable under coverage. Furthermore, neither of these problems vanish asymptotically with increasing the number of clusters or cluster size. These results have major implications for random effects inference, especially if the true random effects distribution is heavier tailed than the normal. Fortunately, simple graphical and goodness‐of‐fit measures of the random effects predictions appear to have reasonable power at detecting misspecification. We apply linear mixed models to a survey of more than 4 000 high school students within 100 schools and analyse how mathematics achievement scores vary with student attributes and across different schools. The application demonstrates the sensitivity of mixed model inference to the true but unknown random effects distribution
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherInternational Statistical Institute
dc.rights© 2020 The Authors. International Statistical Review © 2020 International Statistical Institute
dc.sourceInternational Statistical Review
dc.subjectFixed effects
dc.subjecthypothesis testing
dc.subjectmaximum likelihood
dc.subjectprediction
dc.subjectrobustness
dc.subjectvariance components
dc.titleRandom Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models
dc.typeJournal article
local.description.notesImported from ARIES
dc.date.issued2020
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationa383154xPUB11345
local.type.statusAccepted Version
local.contributor.affiliationHui, Francis, College of Business and Economics, ANU
local.contributor.affiliationMuller, Samuel, University of Sydney
local.contributor.affiliationWelsh, Alan, College of Business and Economics, ANU
local.description.embargo20921-04-15
dc.relationhttp://purl.org/au-research/grants/arc/DP180100836
local.identifier.doi10.1111/insr.12378
dc.date.updated2020-11-02T04:17:15Z
CollectionsANU Research Publications

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