Quiz 3

Mixed Effects Models

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# Mixed Effects Models ## 9.1 Fixed vs. Random Effects Factor Type Levels Inference Example Fixed All levels in study About specific levels Treatment (drug A, B, C) Random Sample of levels About population Subjects (random sample) ## 9.2 Random Intercept Model $$ y_{ij} = \beta_0 + b_{0i} + \beta_1 x_{ij} + \varepsi...

Mixed Effects Models

9.1 Fixed vs. Random Effects

Factor TypeLevelsInferenceExample
FixedAll levels in studyAbout specific levelsTreatment (drug A, B, C)
RandomSample of levelsAbout populationSubjects (random sample)

9.2 Random Intercept Model

yij=β0+b0i+β1xij+εijy_{ij} = \beta_0 + b_{0i} + \beta_1 x_{ij} + \varepsilon_{ij}
Where b0i∼N(0,σb2)b_{0i} \sim N(0, \sigma_b^2) is the random intercept for group ii.

9.3 Mixed Model in Matrix Form

y=Xβ+Zb+ε\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{b} + \boldsymbol{\varepsilon}
Where b∼N(0,G)\mathbf{b} \sim N(0, \mathbf{G}) and ε∼N(0,R)\boldsymbol{\varepsilon} \sim N(0, \mathbf{R}). Join Discord PreviousLogistic RegressionNextModel Comparison
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