Lec17.RandomEffects

Lec17.RandomEffects - Fixed and Random Effects Models KNNL...

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Unformatted text preview: Fixed and Random Effects Models KNNL Chapter 25 Fixed versus Random Effects Fixed Effects ANOVA Models I All levels covered Differences in levels of interest Random Effects ANOVA Models II Levels a sample of all levels Gender Male Female Foot Size 12,10, 11,10 8,9,10, 9 Subject Math English History Scores 77,65, 80 100,99, 75 88,89, 85 Fixed versus Random Effects Fixed Effects Random Effects n j r i N parameters Y ij i ij i ij ,..., 1 ; ,..., 1 ) , ( ~ 2 = = = + = σ ε μ ε μ n j r i N N Y ij i ij i ij ,..., 1 ; ,..., 1 ) , ( ~ ) , ( ~ 2 2 . = = + = σ ε σ μ μ ε μ μ Random Effects Mean and Variance 2 2 2 2 . . } { } { } { } { σ σ σ σ μ μ ε μ ε μ μ + = = = + = + = + = Y ij ij i ij ij i ij Y E E Y E Y Expected Mean Expected Variance Note constant variance Normally distributed Random Effects Covariance Yij are independent only if they pertain to different factor levels ' } , { ' } , { ' ' 2 ' i i Y Y j j Y Y j i ij ij ij ≠ = ≠ = σ σ σ μ Random Effects Variance-Covariance Matrix = = 2 2 2 2 2 2 2 2 2 22 21 12 11 } { Y Y Y Y Y Y Y Y σ σ σ σ σ σ σ σ σ μ μ μ μ Y Y Random Effects Correlation Intraclass correlation coefficient ' } , { 2 2 2 2 2 ' j j Y Y Y ij ij ≠ + = = σ σ σ σ σ ρ μ μ μ Hypothesis Test : : : ... : 2 2 . 2 1 = = = = = μ μ σ σ μ μ μ μ μ A i n H H H H ANOVA Despite the models being different the ANOVA for a random effects study is conducted in an identical way to that for a fixed effects study… at least for a single-factor study MSE MSR F MSE E n MSR E = = + = * 2 2 2 } { } { σ σ σ μ APEX Enterprises Five personnel officers were selected at random, and four prospected employee candidates were assigned at random to each selected officer. Do the personnel officers differ in how they rate employee candidates?...
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Lec17.RandomEffects - Fixed and Random Effects Models KNNL...

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