Multilevel modeling for repeated measures: Difference between revisions

Revision as of 03:49, 16 March 2014

Revision as of 03:52, 19 April 2014

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One application of [[multilevel modeling]] (MLM) is the analysis of repeated measures data. '''Multilevel modeling for repeated measures''' data is most often discussed in the context of modeling change over time (i.e. growth curve modeling for longitudinal designs); however, it may also be used for repeated measures data in which time is not a factor.<ref>{{cite journal|last=Hoffman|first=Lesa|coauthors=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}}</ref>

In multilevel modeling, an overall change function (e.g. linear, quadratic, cubic etc.) is fitted to the whole sample and, just as in multilevel modeling for clustered data, the [[slope]] and [[Y-intercept|intercept]] may be allowed to vary. For example, in a study looking at income growth with age, individuals might be assumed to show linear improvement over time. However, the exact intercept and slope could be allowed to vary across individuals (i.e. defined as random coefficients).

Multilevel modeling with repeated measures employs the same statistical techniques as MLM with clustered data. In multilevel modeling for repeated measures data, the measurement occasions are nested within cases (e.g. individual or subject). Thus, [[Multilevel model#Level 1 regression equation|level-1]] units consist of the repeated measures for each subject, and the [[Multilevel model#Level 1 regression equation|level-2]] unit is the individual or subject. In addition to estimating overall parameter estimates, MLM allows regression equations at the level of the individual. Thus, as a growth curve modeling technique, it allows the estimation of inter-individual differences in intra-individual change over time by modeling the variances and covariances.<ref>{{cite journal|last=Curran|first=Patrick J.|coauthors=Obeidat, Khawla, Losardo, Diane|title=Twelve Frequently Asked Questions About Growth Curve Modeling|journal=Journal of Cognition and Development|date=NaN undefined NaN|volume=11|issue=2|pages=121–136|doi=10.1080/15248371003699969}}</ref> In other words, it allows the testing of individual differences in patterns of responses over time (i.e. growth curves). This characteristic of multilevel modeling makes it preferable to other repeated measures statistical techniques such as repeated measures-analysis of variance ([[RM-ANOVA]]) for certain research questions.

==Assumptions==

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==Statistics & Interpretation==

Mathematically, multilevel analysis with repeated measures is very similar to the analysis of data in which subjects are clustered in groups. However, one point to note is that time-related predictors must be explicitly entered into the model to evaluate trend analyses and to obtain an overall test of the repeated measure. Furthermore, interpretation of these analyses is dependent on the scale of the time variable (i.e. how it is coded).

*'''Fixed Effects:''' Fixed regression coefficients may be obtained for an overall equation that represents how, averaging across subjects, the subjects change over time.

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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.|coauthors=Obeidat, Khawla, 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}}

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*{{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|coauthors=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|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.].}}