Analysis of Covariation :: SAS/STAT(R) 12.1 User's Guide

Analysis of Covariation

When you specify more than one dependent variable, the NESTED procedure produces a descriptive analysis of the covariance between each pair of dependent variables in addition to a separate analysis of variance for each variable. The analysis of covariation is computed under the basic random-effects model for each pair of dependent variables:

$\displaystyle y_{i_1 i_2 \cdots i_ n r}$	$\displaystyle =$	$\displaystyle \mu + \alpha _{i_1} + \beta _{i_1 i_2} + \cdots + \epsilon _{i_1 i_2 \cdots i_ n r}$
$\displaystyle y_{i_1 i_2 \cdots i_ n r}^{\prime }$	$\displaystyle =$	$\displaystyle \mu ^{\prime } + \alpha _{i_1}^{\prime } + \beta _{i_1 i_2}^{\prime } + \cdots + \epsilon _{i_1 i_2 \cdots i_ n r}^{\prime }$

where the notation is the same as that used in the preceding general random-effects model.

There is an additional assumption that all the random effects in the two models are mutually uncorrelated except for corresponding effects, for which

$\displaystyle \mbox{Corr}(\alpha _{i_1} , \alpha _{i_1}^{\prime })$	$\displaystyle =$	$\displaystyle \rho _{\alpha }$
$\displaystyle \mbox{Corr}(\beta _{i_1 i_2}, \beta _{i_1 i_2}^{\prime })$	$\displaystyle =$	$\displaystyle \rho _{\beta }$
$\displaystyle$	$\displaystyle \vdots$	$\displaystyle$
$\displaystyle \mbox{Corr}(\epsilon _{i_1 i_2 \cdots i_ n r}, \epsilon _{i_1 i_2 \cdots i_ n r}^{\prime })$	$\displaystyle =$	$\displaystyle \rho _{\epsilon }$

The NESTED Procedure

Analysis of Covariation