hybrid repeated measures model from Mitchell's Stata for the Behavioral Sciences

[Dave Airey]

In the repeated measures chapter of Michael Mitchell's Stata for the Behaivoral Sciences the author recommends a hybrid ANOVA / mixed model approach where the random effect of subject is dropped using a command like:

mixed y i.treated##i.group || id:, noconst residuals(un, t(time)),

This model fits only one fixed intercept; no random intercepts by id. The predicted values for xb (fixed) and fitted (fixed + random) are consequently the same. The mixed command fits unique residual variances at each time point and unique residual covariances between all time points. The fitted values are the same as for a plain regression if the data are balanced:

regress y treated##i.group

Is Mitchell's recommendation a common one for repeated measures data? Does anyone know of other sources recommending this model?

[Dave Airey]

I found a discussion of this modeling choice digging in the library in West et al., Linear Mixed Models: A Practical Guide... in Chapter 6 where they discussed fitting "marginal models with an unstructured covariance matrix" to the autism data. I can see a use of noconst in Stata on page 277 and some discussion of this marginal model on pages 302-305. The authors view this model as a general linear model with correlated error rather than a mixed model, as there are no random effects.

[Joseph Coveney]

It's essentially an implementation of MANOVA. I've not infrequently seen the analogous set up with SAS's PROC MIXED. The advantage is that you can have missing (at random or completely at random) values and still keep the remaining observations for the ID in the model, unlike with conventional MANOVA, which omits the observations listwise. As to how common, I would conjecture that it's used now frequently wherever MANOVA used to be, unless there are fortuitously no missing data. It's basically favored over MANOVA because of that advantage, coupled with the availability of small-sample adjustments (e.g., Kenward-Roger) to the test statistics and their degrees of freedom.

[Dave Airey]

Thanks for the reply. The SAS example from West et al. was:

title “Marginal Model w/Unstructured Covariance Matrix”;
proc mixed data = autism2 noclprint covtest;
class childid sicdegp age;
model vsae = sicdegp age_2 age_2sq age_2*sicdegp / solution;
repeated age / subject = childid type = un r rcorr;
run;

In R, gls() is used for a similar marginal model.