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Linear Mixed-Effects Regression - Statistics

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Linear Mixed-Effects RegressionNathaniel E. HelwigAssistant Professor of Psychology and StatisticsUniversity of Minnesota (Twin Cities)Updated 04-Jan-2017Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 1CopyrightCopyright 2017 by Nathaniel E. HelwigNathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 2Outline of Notes1) Correlated Data:Overview of problemMotivating ExampleModeling correlated data2) One-Way RM- anova : model Form & AssumptionsEstimation & InferenceExample: Grocery Prices3) Linear Mixed-Effects model :Random Intercept ModelRandom Intercepts & SlopesGeneral FrameworkCovariance StructuresEstimation & InferenceExample: TIMSS DataNathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 3Correlated DataCorrelated DataNathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 4Correlated DataOverview of ProblemWhat are Correlated Data?

One-Way Repeated Measures ANOVA Model Form and Assumptions Compound Symmetry Assumptions imply covariance pattern known ascompound symmetry All repeated measurements have same variance All pairs of repeated measurements have same covariance With a = 4 repeated measurements the covariance matrix is Cov(yi) = 0 B B @ ˙2 Y!˙ 2 Y!˙ 2 Y!˙ 2 Y ...

  Model, Measure, Mixed, Repeated, Anova, Repeated measures anova model

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