*! version 1.0.0 26jun2011
help xtmixed_corr

Title

xtmixed_corr -- Model-implied intracluster correlations after xtmixed

Syntax

xtmixed_corr [, options]

options

Main
at(at_spec) specify level values; the default is the first level-two cluster

all correlations for all the data

list list model data corresponding to displayed correlations

nosort list matrices in the row order as listed in the data

format(format) specify display format

matlist_options style options for displaying matrices;
see [P] matlist

Description

Linear mixed models as fit by xtmixed have complex expressions for
intracluster correlation. Correlation comes from two sources: (1)
the design of the random effects and their assumed covariance
from the multiple levels in your model; and (2) the correlation structure of
the residuals, whether they be treated as independent, auto-regressive,
Toeplitz, etc. Residuals may also be modeled as heteroskedastic; see
xtmixed for details.

xtmixed_corr is designed to combine all sources of correlation
into one overall correlation matrix for a given cluster (or for a given
group of clusters, if you wish). This allows you to compare different
multilevel models in terms of the ultimate intracluster correlation matrix
that each model implies.

Options

Main

at(at_spec), where at_spec is

level_var = value [ level_var = value ...]

specifies the cluster of observations for which you want the intracluster
correlation matrix.

For example, if you specify

. xtmixed_corr, at(school = 33)

you get the intracluster correlation matrix for those observations
in school 33. If you specify,

. xtmixed_corr, at(school = 33 classroom = 4)

you get the correlation matrix for classroom 4 in school 33.

If at() is not specified, then you get the correlations
for the first level-two cluster encountered in the data. This is
usually what you want.

all specifies that you want the correlation matrix for all
the data. This is not recommended unless you have a relatively small dataset
or you enjoy seeing large N x N matrices. However, this can prove
useful in some cases.

list lists the model data for those observations depicted in
the displayed correlation matrix. This option is useful if you have many
random-effects design variables (Z's in xtmixed terminology) and you
wish to see the represented values of these design variables.

nosort lists the rows and columns of the correlation matrix in
the order that they were originally present in the data. Normally,
xtmixed_corr will first sort the data according to level variables,
by-group variables, and time variables in order to produce correlation matrices
whose rows and columns follow a natural ordering. nosort
suppresses this.

format(format) sets the display format for the
standard-deviation vector and correlation matrix. The default is
%6.3f.

matlist_options control how matrices are displayed. See
[P] matlist for details.

Remarks

The intracluster variance-covariance matrix is given by V = Z*Psi*Z' +
R, where Z is the design matrix for the random effects, Psi is the
variance-covariance matrix of the random effects, and R is the residual
variance-covariance matrix. xtmixed_corr performs this
calculation for the data subset that you specify and displays the
resulting standard deviations and correlations based on V.

Examples

Setup

. webuse pig, clear

Random-intercept model, analogous to xtreg

. xtmixed weight week || id:

. xtmixed_corr

Random-intercept and random-slope (coefficient) model

. xtmixed weight week || id: week, cov(un)

. xtmixed_corr, at(id = 33)

Setup

. webuse productivity, clear

Three-level model, observations nested within state nested within region

. xtmixed gsp private emp hwy water other unemp || region: ||
state:

. xtmixed_corr, at(region = 2 state = 28)

. xtmixed_corr, at(region = 2) format(%5.2f)

Setup

. webuse pig, clear

Crossed random effects

. xtmixed weight week || _all: R.week || id:

. xtmixed_corr

Setup

. use http://www.stata-press.com/data/mlmus2/wagepan, clear

. gen educt = educ - 12

. gen yeart = year - 1980

Linear mixed model with AR 1 errors

. xtmixed lwage black hisp union yeart educt || nr:, nocons res(ar 1, t(yeart))

. xtmixed_corr

Setup

. webuse ovary, clear

. keep if time<=7

Linear mixed model with MA 2 errors

. xtmixed follicles sin1 cos1 || mare: sin1, residuals(ma 2, t(time))

. xtmixed_corr, list

Setup

. webuse childweight, clear

Linear mixed model with heteroskedastic error variances

. xtmixed weight age || id:age, cov(un) residuals(independent, by(girl))

. xtmixed_corr, list

. xtmixed_corr, at(id=4108) list

Saved results

xtmixed_corr saves the following in r():

Matrices

r(sd) standard deviations

r(corr) correlation

r(V) variance-covariance

r(psi) variance-covariance of random effects

r(Z) model-based design matrix

r(R) variance-covariance matrix of level-one errors

Also see

Help: [XT] xtmixed; [XT] xtmixed postestimation