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From |
David Airey <david.airey@Vanderbilt.Edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: specifying linear mixed-effects covariance structure |

Date |
Fri, 19 Oct 2007 07:45:17 -0500 |

There is not the wide array of covariance structures available in Stata xtmixed as in SAS Proc Mixed. But your documentation should make this clear. There are four currently available:

vartype description

------------------------------------------------------------------------ ---------------

independent one variance parameter per random effect, all covariances

zero; the default unless a factor variable is specified

exchangeable equal variances for random effects, and one common pairwise

covariance

identity equal variances for random effects, all covariances zero; the

default for factor variables

unstructured all variances-covariances distinctly estimated

------------------------------------------------------------------------ ---------------

You can combine these, but I don't see how useful that is. Stata Corp did say more can be expected, but I think they made categorical dependent variable mixed models a priority.

-Dave

On Oct 18, 2007, at 4:05 PM, jwegelin wrote:

The purpose of this email is to enquire regarding the capabilities of

Stata for specifying the covariance structure in linear mixed-effects

models. The email starts with a fairly detailed description of the

problem and a sketch of how one approaches it in SAS. We end with a set

of questions regarding Stata, marked by asterisks *********.

The bottom line is, "Can I do this all in Stata, or do I need to use SAS

for such analyses?"

EXPOSITION / PROBLEM DESCRIPTION.

Suppose you have a longitudinal outcome (K repeated measures on N units)

and are fitting a linear mixed-effects model. Suppose you have specified

random intercepts and random slopes.

For instance, in Stata this might look like

xi: xtmixed Size i.Tribe*Day || Mouse: Day, cov(un)

where Tribe is dichotomous ("case" or "control"), Day goes from zero to

ten, and each Mouse, belonging to one of the Tribes, is measured each

day. You want to know whether the growth patterns differ between Tribes.

(1) One might consider the possibility of autocorrelation of residuals

within unit (within Mouse) over time, for instance an AR(1)

autoregressive model; or one might want to try conjugate symmetry as

another alternative to independence of the within-Mouse residuals.

In SAS PROC MIXED it is possible to specify AR(1), exchangeable,

conjugate symmetry and other kinds of variances of the within-Mouse

residuals under the REPEATED statement, TYPE=AR(1), etc.

(2) One might suspect---e.g., from initial exploratory graphics---that

the variance of the "case" Tribe exceeds that of the "control" Tribe.

Furthermore, one might be curious whether this difference in variance is

in the intercept and slope random effects only, in the residuals only,

or in both.

In SAS PROC MIXED one can allow different variances of the random slopes

and intercepts in the two Tribes by saying "GROUP=TRIBE" under the

RANDOM statement.

Separately, one can allow different variances of the within-Mouse

residuals by saying the same thing under the REPEATED statement.

(3) Further, one can separately specify the covariance structures of the

between-mouse random effects (the slope and intercept random effects) on

one hand and the within-mouse residuals on the other hand.

When I used SAS, I specified unrestricted ("unstructured" in SAS- speak)

covariance of the slopes and intercepts within each Tribe. This used

three degrees of freedom per Tribe and permitted the random Mouse

intercept to be correlated with the random Mouse slope. But I specified

a much more restricted structure for the within-mouse residuals, since

that matrix is 10 by 10.

**************************

QUESTIONS REGARDING STATA:

Am I correct in believing that there is no procedure or option in Stata

by which one can readily do either of (1) or (2) described above?

If this is correct, are there any plans, either in Stata proper or among

people making well-documented add-ons (see for instance the work of

Rabe-Hesketh), to add these features?

In current xtmixed, we can specify the between-Mouse variance of

the random effects as "independent", "exchangeable", "identity" or

"unstructured". (See http://www.stata.com/help.cgi?xtmixed for lucid

definitions.) Regarding the within-Mouse residual variance, am I correct

in guessing that it is always specified as "identity" when one runs xtmixed?

In Stata, the xtreg procedure allows us to specify the within-group

(within-Mouse) correlation structure as autoregressive, exchangeable, or

conjugate symmetry, but only with the "pa" (population average) option,

I believe. One does this with the "corr" option. But I think there is no

"corr" option in xtmixed. Furthermore, I think that one can only specify

random intercepts, not other random effects, under xtreg.

Thanks in advance for any information or correction.

Jacob A. Wegelin

Assistant Professor

Department of Biostatistics

Virginia Commonwealth University

730 East Broad Street Room 3006

P. O. Box 980032

Richmond VA 23298-0032

U.S.A.

http://www.people.vcu.edu/~jwegelin

jwegelin@vcu.edu

*

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-- David C. Airey, Ph.D. Pharmacology Research Assistant Professor Center for Human Genetics Research Member Department of Pharmacology School of Medicine Vanderbilt University Rm 8158A Bldg MR3 465 21st Avenue South Nashville, TN 37232-8548 TEL (615) 936-1510 FAX (615) 936-3747 EMAIL david.airey@vanderbilt.edu URL http://people.vanderbilt.edu/~david.c.airey/dca_cv.pdf URL http://www.vanderbilt.edu/pharmacology * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: specifying linear mixed-effects covariance structure***From:*jwegelin <jwegelin@vcu.edu>

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