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Linear Mixed-Effects Regression - Statistics

Linear Mixed-Effects RegressionNathaniel E. HelwigAssistant Professor of Psychology and StatisticsUniversity of Minnesota (Twin Cities)Updated 04-Jan-2017 Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 1 CopyrightCopyright 2017 by Nathaniel E. HelwigNathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects RegressionUpdated 04-Jan-2017 : Slide 2 Outline 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.

One-Way Repeated Measures ANOVA Estimation and Inference Extended ANOVA Table and F Tests We typically organize the SS information into an ANOVA table: Source SS df MS F p-value SSS a P n i=1 ˆ^ 2 i n 1 MSS F sp SSA n P a j=1 ^ 2 j a 1 MSA F a p a SSE P a j=1 P n i=1 (yij y^ jk) 2 (n 1)(a 1) MSE SST P a j=1 n i=1 (yij y) 2 na 1 MSS = SSS n 1 ...

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