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I was wondering what the definition of a variance component model is? I searched it online, and found it often appears with mixed-effect models, but couldn't understand what it is, and how it is different from and related to mixed-effect models.

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Variance component models "estimate the variability accounted for by each level of the hierarchy". They can refer to mixed (fixed and random) intercept models, in the form of $$y_{ij}=\beta_0+u_i+\epsilon_{ij},$$ where $u_i∼N(0,\sigma_u^2),\epsilon_{ij}∼N(0,\sigma_{\epsilon}^2)$ are the two variance components.

References:

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    $\begingroup$ Solid. I'd add (1) Variance-component models are explicitly designed to model within cluster correlations (2) as above I've usually used the term for random effects models without covariates. $\endgroup$
    – charles
    Dec 15, 2013 at 1:39
  • $\begingroup$ Thanks, @charles! I completely agree with you about the first point. For (2), I think a) generally speaking the intercept is also a covariate; b) do variance component models allow random slopes (i.e. covariates for random effects)? $\endgroup$
    – Randel
    Dec 15, 2013 at 4:49

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