Random and Mixed Effects ANOVA

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Presentation transcript:

Random and Mixed Effects ANOVA KNNL – Chapter 25

1-Way Random Effects Model In some settings, the levels of the factor in a 1-Way ANOVA model are a random sample from a larger population of levels Goal is to make statements regarding the population of levels, as opposed to only regarding the levels in the study. We wish to make statements about the variation in the effects of the levels Studies are often interested in measuring reliability of testing/measuring procedures

Statistical Model / Parameters of Interest

Analysis of Variance - I

Analysis of Variance - II

Estimating Overall Mean m•

Estimating Intra-Class Correlation rI = sm2 / sY2

Estimating Within Group Variance: s2

Estimating Between Group Variance: sm2

2-Way Random Effects Model

2-Way Mixed Effects Model

Expected Mean Squares for 2-Way ANOVA

Tests for Main Effects and Interactions

Estimating Variance Components

Estimating Fixed Effects in Mixed Model

Estimating Marginal (Factor A) Means in Mixed Models