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From |
jwegelin <jwegelin@vcu.edu> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 18 Oct 2007 17:05:43 -0400 |

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 * * 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/

**Follow-Ups**:**Re: st: specifying linear mixed-effects covariance structure***From:*David Airey <david.airey@Vanderbilt.Edu>

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