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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. 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 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, level-1 units consist of the repeated measures for each subject, and the 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. 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== The 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 functions). 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multilevel modeling for repeated measures」の詳細全文を読む スポンサード リンク
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