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Mixed Effects Models

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Now · 9.1 Fixed vs. Random Effects

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)

y_{ij} = \beta_0 + b_{0i} + \beta_1 x_{ij} + \varepsilon_{ij}

Where

b_{0i} \sim N(0, \sigma_b^2)

is the random intercept for group

i

\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{Z}\mathbf{b} + \boldsymbol{\varepsilon}

Where

\mathbf{b} \sim N(0, \mathbf{G})

and

\boldsymbol{\varepsilon} \sim N(0, \mathbf{R})