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[ME] Multilevel Mixed Effects - Stata

Stata Multilevel Mixed -EFFECTSREFERENCE MANUALRELEASE 13 A Stata Press PublicationStataCorp LPCollege Station, Texas Copyrightc 1985 2013 StataCorp LPAll rights reservedVersion 13 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in TEXISBN-10: 1-59718-119-6 ISBN-13: 978-1-59718-119-8 This manual is protected by copyright. All rights are reserved. No part of this manual may be reproduced, storedin a retrieval system, or transcribed, in any form or by any means electronic, mechanical, photocopy, recording, orotherwise without the prior written permission of StataCorp LP unless permitted subject to the terms and conditionsof a license granted to you by StataCorp LP to use the software and documentation.

Cross-referencing the documentation When reading this manual, you will find references to other Stata manuals. For example, [U] 26 Overview of Stata estimation commands[R] regress[D] reshapeThe first example is a reference to chapter 26, …

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Transcription of [ME] Multilevel Mixed Effects - Stata

1 Stata Multilevel Mixed -EFFECTSREFERENCE MANUALRELEASE 13 A Stata Press PublicationStataCorp LPCollege Station, Texas Copyrightc 1985 2013 StataCorp LPAll rights reservedVersion 13 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in TEXISBN-10: 1-59718-119-6 ISBN-13: 978-1-59718-119-8 This manual is protected by copyright. All rights are reserved. No part of this manual may be reproduced, storedin a retrieval system, or transcribed, in any form or by any means electronic, mechanical, photocopy, recording, orotherwise without the prior written permission of StataCorp LP unless permitted subject to the terms and conditionsof a license granted to you by StataCorp LP to use the software and documentation.

2 No license, express or implied,by estoppel or otherwise, to any intellectual property rights is granted by this provides this manual as is without warranty of any kind, either expressed or implied, including, butnot limited to, the implied warranties of merchantability and fitness for a particular purpose. StataCorp may makeimprovements and/or changes in the product(s) and the program(s) described in this manual at any time and software described in this manual is furnished under a license agreement or nondisclosure agreement. The softwaremay be copied only in accordance with the terms of the agreement. It is against the law to copy the software ontoDVD, CD, disk, diskette, tape, or any other medium for any purpose other than backup or archival automobile dataset appearing on the accompanying media is Copyrightc 1979 by Consumers Union of ,Inc.

3 , Yonkers, NY 10703-1057 and is reproduced by permission from CONSUMER REPORTS, April ,, Stata Press, Mata,, and NetCourse are registered trademarks of StataCorp and Stata Press are registered trademarks with the World Intellectual Property Organization of the United is a trademark of StataCorp brand and product names are registered trademarks or trademarks of their respective copyright information about the software, typehelp copyrightwithin suggested citation for this software isStataCorp. : Release 13. Statistical Software. College Station, TX: StataCorp .. Introduction to Multilevel Mixed - Effects models1mecloglog .. Multilevel Mixed - Effects complementary log-log regression37mecloglog postestimation.

4 Postestimation tools for mecloglog51meglm .. Multilevel Mixed - Effects generalized linear model56meglm postestimation .. Postestimation tools for meglm81melogit .. Multilevel Mixed - Effects logistic regression98melogit postestimation .. Postestimation tools for melogit 112menbreg .. Multilevel Mixed - Effects negative binomial regression 120menbreg postestimation .. Postestimation tools for menbreg 137meologit .. Multilevel Mixed - Effects ordered logistic regression 141meologit postestimation .. Postestimation tools for meologit 155meoprobit .. Multilevel Mixed - Effects ordered probit regression 160meoprobit postestimation .. Postestimation tools for meoprobit 174mepoisson .. Multilevel Mixed - Effects Poisson regression 179mepoisson postestimation.

5 Postestimation tools for mepoisson 193meprobit .. Multilevel Mixed - Effects probit regression 197meprobit postestimation .. Postestimation tools for meprobit 210meqrlogit .. Multilevel Mixed - Effects logistic regression (QR decomposition) 218meqrlogit postestimation .. Postestimation tools for meqrlogit 242meqrpoisson .. Multilevel Mixed - Effects Poisson regression (QR decomposition) 258meqrpoisson postestimation .. Postestimation tools for meqrpoisson 276mixed .. Multilevel Mixed - Effects linear regression 285mixed postestimation .. Postestimation tools for Mixed 336 Glossary ..355 Subject and author index ..359iCross-referencing the documentationWhen reading this manual, you will find references to other Stata manuals.

6 For example,[U] 26 Overview of Stata estimation commands[R]regress[D]reshapeThe first example is a reference to chapter 26,Overview of Stata estimation commands, in theUser sGuide; the second is a reference to theregressentry in theBase Reference Manual; and the thirdis a reference to thereshapeentry in theData Management Reference the manuals in the Stata Documentation have a shorthand notation:[GSM]Getting Started with Stata for Mac[GSU]Getting Started with Stata for Unix[GSW]Getting Started with Stata for Windows[U] Stata User s Guide[R] Stata Base Reference Manual[D] Stata Data Management Reference Manual[G] Stata Graphics Reference Manual[XT] Stata Longitudinal-Data/Panel-Data Reference Manual[ME] Stata Multilevel Mixed - Effects Reference Manual[MI] Stata Multiple-Imputation Reference Manual[MV] Stata Multivariate Statistics Reference Manual[PSS] Stata Power and Sample-Size Reference Manual[P] Stata Programming Reference Manual[SEM] Stata Structural Equation Modeling Reference Manual[SVY] Stata Survey Data Reference Manual[ST] Stata Survival Analysis and Epidemiological Tables Reference Manual[TS] Stata Time-Series Reference Manual[TE]

7 Stata Treatment- Effects Reference Manual:Potential Outcomes/Counterfactual Outcomes[I] Stata Glossary and Index[M]Mata Reference ManualiiiTitleme Introduction to Multilevel Mixed - Effects modelsSyntax by exampleFormal syntaxDescriptionRemarks and examplesAcknowledgmentsReferencesAlso seeSyntax by exampleLinear Mixed - Effects modelsLinear model ofyonxwith random intercepts byidmixed y x || id:Three-level linear model ofyonxwith random intercepts bydoctorandpatientmixed y x || doctor: || patient:Linear model ofyonxwith random intercepts and coefficients onxbyidmixed y x || id: xSame model with covariance between the random slope and interceptmixed y x || id: x, covariance(unstructured)Linear model ofyonxwith crossed random Effects foridandweekmixed y x || _all: || _all: model specified to be more computationally efficientmixed y x || _all: || week:Full factorial repeated-measuresANOVA ofyonaandbwith random Effects byfieldmixed y a##b || field:Generalized linear Mixed - Effects modelsLogistic model ofyonxwith random intercepts byid, reporting odds ratiosmelogit y x || id: , orSame model specified as aGLMmeglm y x || id:, family(bernoulli) link(logit)Three-level ordered probit model ofyonxwith random intercepts bydoctorandpatientmeoprobit y x || doctor: || patient.

8 12 me Introduction to Multilevel Mixed - Effects modelsFormal syntaxLinear Mixed - Effects modelsmixeddepvar feequation[||reequation] [|| ] [,options]where the syntax of the fixed- Effects equation,feequation, is[indepvars] [if] [in] [weight] [,feoptions]and the syntax of a random- Effects equation,reequation, is the same as below for a generalizedlinear Mixed - Effects linear Mixed - Effects modelsmecmd depvar feequation[||reequation] [|| ] [,options]where the syntax of the fixed- Effects equation,feequation, is[indepvars] [if] [in] [,feoptions]and the syntax of a random- Effects equation,reequation, is one of the following:for random coefficients and interceptslevelvar:[varlist] [,reoptions]for random Effects among the values of a factor variablelevelvar: a variable identifying the group structure for the random Effects at that level or isallrepresenting one group comprising all models are characterized as containing both fixed Effects and random Effects .

9 Thefixed Effects are analogous to standard regression coefficients and are estimated directly. The randomeffects are not directly estimated (although they may be obtained postestimation) but are summarizedaccording to their estimated variances and covariances. Random Effects may take the form of eitherrandom intercepts or random coefficients, and the grouping structure of the data may consist ofmultiple levels of nested groups. As such, Mixed - Effects models are also known in the literature asmultilevel models and hierarchical models. Mixed - Effects commands fit Mixed - Effects models for avariety of distributions of the response conditional on normally distributed random Introduction to Multilevel Mixed - Effects models 3 Mixed - Effects linear regressionmixedMultilevel Mixed - Effects linear regressionMixed- Effects generalized linear modelmeglmMultilevel Mixed - Effects generalized linear modelMixed- Effects binary regressionmelogitMultilevel Mixed - Effects logistic regressionmeqrlogitMultilevel Mixed - Effects logistic regression (QRdecomposition)

10 MeprobitMultilevel Mixed - Effects probit regressionmecloglogMultilevel Mixed - Effects complementary log-log regressionMixed- Effects ordinal regressionmeologitMultilevel Mixed - Effects ordered logistic regressionmeoprobitMultilevel Mixed - Effects ordered probit regressionMixed- Effects count-data regressionmepoissonMultilevel Mixed - Effects Poisson regressionmeqrpoissonMultilevel Mixed - Effects Poisson regression (QRdecomposition)menbregMultilevel Mixed - Effects negative binomial regressionMixed- Effects multinomial regressionAlthough there is nomemlogitcommand, Multilevel Mixed - Effects multinomiallogistic models can be fit usinggsem; see [SEM]example and examplesRemarks are presented under the following headings:IntroductionUsing Mixed - Effects commandsMixed- Effects modelsLinear Mixed - Effects modelsGeneralized linear Mixed - Effects modelsAlternative Mixed - Effects model specificationLikelihood calculationComputation time and the Laplacian approximationDiagnosing convergence problemsDistribution theory for likelihood-ratio testExamplesTwo-level modelsCovariance structuresThree-level modelsCrossed- Effects models4 me Introduction to Multilevel Mixed - Effects modelsIntroductionMultilevel models have been used extensively in diverse fields, from the health and social sciencesto econometrics.


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