General Random Effects Model

The NESTED Procedure

A random effects model for data from a completely nested design with n factors has the general form

$y_{i_1 i_2 ... i_n r} = \mu + \alpha_{i_1} + \beta_{i_1 i_2} + ... + \epsilon_{i_1 i_2 ... i_n r}$

where

y_{i₁ i₂ ... i_n r}: is the value of the dependent variable observed at the rth replication with factor j at level i_j, for j = 1, ... ,n.
$\mu$: is the overall (fixed) mean of the sampled population.
$\alpha_{i_1},\beta_{i_1 i_2}, ... , \epsilon_{i_1 i_2 ... i_n r}$: are mutually uncorrelated random effects with zero means and respective variances $\sigma_{\alpha}^2$ , $\sigma_{\beta}^2$ , ..., $\sigma_{\epsilon}^2$ .