# What is a variance component model?

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.

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:

• 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. Dec 15, 2013 at 1:39
• 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)? Dec 15, 2013 at 4:49