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|coauthors=van den Bergh, Huub|title=On multi-level modeling of data from repeated measures designs: a tutorial|journal=Speech Communication|date=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 [[homoschedasticity]];, constant covariances (compound symmetry), or constant variances of differences scores ([[sphericity]]) are violated for RM-ANOVA. MLM allows for 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>

::Violation of the variance and covariance assumptions in RM-ANOVA suggests that there are “unaccounted for’ individual differences in change over time”<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>. This has two important implications, which may be addressed with MLM, because MLM allows for inspection of the variances and covariances under different treatment conditions: (1) the individual differences in change over time may be related to other measured variables; and (2) taking the individual differences into account will make the statistical tests more appropriate

::'''2. MLM Allows for 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.

::'''3. MLM can Handle Missing Data:''' Missing data is permitted in MLM without causing additional complications. With RM-ANOVA, subject’s data must be excluded if they are missing a single data point. Missing data and attempts to resolve missing data (i.e. using the subject’s mean for non-missing data) can raise additional problems in RM-ANOVA.