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:

StartLayout 1st Row 1st Column y Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r 2nd Column equals 3rd Column mu plus alpha Subscript i 1 Baseline plus beta Subscript i 1 i 2 Baseline plus midline-horizontal-ellipsis plus epsilon Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r 2nd Row 1st Column y prime Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r 2nd Column equals 3rd Column mu prime plus alpha prime Subscript i 1 Baseline plus beta prime Subscript i 1 i 2 Baseline plus midline-horizontal-ellipsis plus epsilon prime Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r EndLayout

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

StartLayout 1st Row 1st Column Corr left-parenthesis alpha Subscript i 1 Baseline comma alpha prime Subscript i 1 right-parenthesis 2nd Column equals 3rd Column rho Subscript alpha 2nd Row 1st Column Corr left-parenthesis beta Subscript i 1 i 2 Baseline comma beta prime Subscript i 1 i 2 right-parenthesis 2nd Column equals 3rd Column rho Subscript beta 3rd Row 1st Column Blank 2nd Column vertical-ellipsis 3rd Column Blank 4th Row 1st Column Corr left-parenthesis epsilon Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r Baseline comma epsilon prime Subscript i 1 i 2 midline-horizontal-ellipsis i Sub Subscript n Subscript r right-parenthesis 2nd Column equals 3rd Column rho Subscript epsilon EndLayout
Last updated: December 09, 2022