Multilevel modeling for repeated measures: Difference between revisions

Revision as of 03:52, 19 April 2014

Revision as of 11:50, 18 July 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|coauthorsauthor2=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).

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The [[statistical assumptions|assumptions]] of MLM that hold for clustered data also apply to repeated measures:

:(1) Random components are assumed to have a normal distribution with a mean of zero

:(2) The dependent variable is assumed to be normally distributed. ''However,'' binary and discrete dependent variables may be examined in MLM using specialized procedures (i.e. employ different [[link function]]s).<ref>{{cite book|last=Snijders|first=Tom A.B.|title=Multilevel analysis : an introduction to basic and advanced multilevel modeling|year=2002|publisher=Sage Publications|___location=London|isbn=978-0761958901|edition=Reprint.|coauthorsauthor2=Bosker, Roel J.}}</ref>

One of the assumptions of using MLM for growth curve modeling is that all subjects show the same relationship over time (e.g. linear, quadratic etc.). Another assumption of MLM for growth curve modeling is that the observed changes are related to the passage of time.<ref name=hox>{{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.].}}</ref>

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::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.

::''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.|coauthorsauthor2=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>

===Multilevel Modeling versus Structural Equation Modeling (SEM; Latent Growth Model)===

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*{{cite journal|last=Singer|first=J. D.|title=Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models|journal=Journal of Educational and Behavioral Statistics|year=1998|volume=23|issue=4|pages=323–355|doi=10.3102/10769986023004323}}

*{{cite book|last=Willett|first=Judith D. Singer, John B.|title=Applied longitudinal data analysis : modeling change and event occurrence|year=2003|publisher=Oxford University Press|___location=Oxford|isbn=0195152964}}

*{{cite book|last=Snijders|first=Tom A.B.|title=Multilevel analysis : an introduction to basic and advanced multilevel modeling|year=2002|publisher=Sage Publications|___location=London|isbn=978-0761958901|edition=Reprint.|coauthorsauthor2=Bosker, Roel J.}}

==Notes==

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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|coauthorsauthor2=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.}}

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*{{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.].}}

*{{cite journal|last=Overall|first=John E.|coauthorsauthor2=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}}

*{{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}}