Multilevel modeling for repeated measures: Difference between revisions

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Repeated measures analysis of variance ([[RM-ANOVA]]) has been traditionally used for analysis of [[repeated measures]] designs. However, violation of the assumptions of RM-ANOVA can be problematic. Multilevel modeling (MLM) is commonly used for repeated measures designs because it presents an alternative approach to analyzing this type of data with three main advantages over RM-ANOVA:<ref name=quene>{{cite journal|last=Quené|first=Hugo|author2=van den Bergh, Huub|title=On multi-level modeling of data from repeated measures designs: a tutorial|journal=Speech Communication|year=2004|volume=43|issue=1-2|pages=103–121|doi=10.1016/j.specom.2004.02.004}}</ref>

::'''1. MLM has Less Stringent Assumptions:''' MLM can be used if the assumptions of constant variances (homogeneity of variance, or [[homoscedasticity]]), constant covariances (compound symmetry), or constant variances of differences scores ([[sphericity]]) are violated for RM-ANOVA. MLM allows modeling of the variance-covariance matrix from the data; thus, unlike in RM-ANOVA, these assumptions are not necessary.<ref name=cohen>{{cite book|first=Jacob Cohen|title=Applied multiple regression/correlation analysis for the behavioral sciences|publisher=Erlbaum|___location=Mahwah, NJ [u.a.]|isbn=9780805822236|edition=3. ed.}}</ref>

::'''2. MLM Allows Hierarchical Structure:''' MLM can be used for higher-order sampling procedures, whereas RM-ANOVA is limited to examining two-level sampling procedures. In other words, MLM can look at repeated measures within subjects, within a third level of analysis etc., whereas RM-ANOVA is limited to repeated measures within subjects.

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::'''4 MLM can also handle data in which there is variation in the exact timing of data collection''' (i.e. variable timing versus fixed timing). For example, data for a longitudinal study may attempt to collect measurements at age 6 months, 9 months, 12 months, and 15 months. However, participant availability, bank holidays, and other scheduling issues may result in variation regarding when data is collected. This variation may be addressed in MLM by adding “age” into the regression equation. There is also no need for equal intervals between measurement points in MLM.

::'''5. MLM is relatively easily extended to discrete data.''' <ref> {{cite book | last = Molenberghs | first = Geert | title = Models for discrete longitudinal data | publisher = Springer Science+Business Media, Inc | ___location = New York | year = 2005 | isbn = 978-0387251448 }} </ref>

::''Note:'' Although [[missing data]] is permitted in MLM, it is assumed to be missing at random. Thus, systematically missing data can present problems.<ref name=quene /><ref>{{cite journal|last=Overall|first=John E.|author2=Tonidandel, Scott|title=Analysis of Data from a Controlled Repeated Measurements Design with Baseline-Dependent Dropouts|journal=Methodology: European Journal of Research Methods for the Behavioral and Social Sciences|year=2007|volume=3|issue=2|pages=58–66|doi=10.1027/1614-2241.3.2.58}}</ref><ref>{{cite journal|last=Overall|first=John|coauthors=Ahn, Chul, Shivakumar, C., Kalburgi, Yallapa|title=PROBLEMATIC FORMULATIONS OF SAS PROC.MIXED MODELS FOR REPEATED MEASUREMENTS|journal=Journal of Biopharmaceutical Statistics|year=2007|volume=9|issue=1|pages=189–216|doi=10.1081/BIP-100101008}}</ref>

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==References==

*{{cite book|first1=Jacob|last1=Cohen|first2=Patricia|last2=Cohen|first3=Stephen G.|last3= West|first4=Leona S.|last4= Aiken |year=2002|title=Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences|publisher=Routledge Academic|isbn=9780805822236|edition=3. ed.}}

*{{cite journal|last=Curran|first=Patrick J. |author2=Obeidat, Khawla |author3=Losardo, Diane|title=Twelve Frequently Asked Questions About Growth Curve Modeling|journal=Journal of Cognition and Development|year=2010|volume=11|issue=2|pages=121–136|doi=10.1080/15248371003699969}}

*{{cite book|last1=Fidell|first1=Barbara G.|last2= Tabachnick|first2= Linda S.|title=Using Multivariate Statistics|year=2007|publisher=Pearson/A & B|___location=Boston ; Montreal|isbn=0205459382|edition=5th ed.}}

*{{cite journal|last=Hoffman|first=Lesa|author2=Rovine, Michael J.|title=Multilevel models for the experimental psychologist: Foundations and illustrative examples|journal=Behavior Research Methods|year=2007|volume=39|issue=1|pages=101–117|doi=10.3758/BF03192848}}

*{{cite book|last=Howell|first=David C.|title=Statistical methods for psychology|year=2010|publisher=Thomson Wadsworth|___location=Belmont, CA|isbn=978-0-495-59784-1|edition=7th ed.}}

*{{cite book|last=Hox|first=Joop|authorlink=Joop Hox|title=Multilevel and SEM Approached to Growth Curve Modeling|year=2005|publisher=Wiley|___location=Chichester|isbn=978-0-470-86080-9|url=http://joophox.net/publist/ebs05.pdf|edition=[Repr.].}}