Analysis of Covariation

The NESTED Procedure

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:

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

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

${Corr}(\alpha_{i_1} , \alpha_{i_1}^') & = & \rho_{\alpha} \ {Corr}(\beta_{i_1 i... ...i_1 i_2 ... i_n r} , \epsilon_{i_1 i_2 ... i_n r}^') & = & \rho_{\epsilon} \$

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