[R-sig-ME] weighting nlme and multivariate outcomes

Afshartous, David DAfshartous at med.miami.edu
Wed Aug 19 16:29:08 CEST 2009


RE defining weights, see section 5.2.1 in Pinheiro & Bates (Mixed Effects Models in S and S-Plus).
RE correlation structures, see section 5.3.3.   While these sections are with respect to the univariate mixed model, note that the multivariate mixed model is analogous to the univariate mixed model that is stratified per some grouping such as say gender.  For instance, as far as the data structure goes, there is no difference if we have 2 variables on 10 subjects over time versus  1 variable on 10 subjects over time for males and females.   Of course, the different scenarios will most likely lead to different model assumptions.

While I haven't used the corrrelation = corSymm for a multivariate mixed model in nlme, I have used varIdent to specify different error variances for the different response variables in the multivariate setting.  Just set up your model as specified in the Doran & Lockwood reference below, and include weights = varIdent(form ~ weights = Ind), where Ind is an indicator variable that identifies each separate response variable. What I would like to do is have the error variances also correlated across the different response variables, but only when they are both measured at the same time point.  I'll check this out again and let you know if this and your structure is possible.

Although it's respect to SAS, a good reference that provides insight into the various assumptions in the multivariate mixed model and the resulting structure of the covariance matrices is:
On the use of PROC MIXED to Estimate Correlation in the Presence of Repeated Measures by Hamlett, Ryan, and Wolfinger (comes up via google)


On 8/18/09 7:14 AM, "Mollet, Fabian" <Fabian.Mollet at wur.nl> wrote:

Dear nlme expert

We need two pieces of information about the fitting of a nlme model which we cannot extract from the R help files and would be most grateful if you could help us. We fit an energy allocation growth model with 4 parameters to individual growth curves using the nlme routine. We thus have repeated age and size measurements of individuals and therefore allow for random individual effects (i.e. the data is grouped by individual).

1)      Because the sampling of these individuals was size stratified we have to account for the representation of the individual in the true size distribution by statistical weighting. The statistical weight would thus differ across individuals but be the same over the repeated measurements of each individual (to which the random effects apply) and should be somehow multiplied by the residuals of the repeated measurements of each individual. We guess we need to use the varClasses argument but it does not seem clear in the R help files to which level the statistical weights would apply. Could you please tell us how to define the statistical weights on the level of the random effects, i.e. on the level of the individual? varIdent?

2)      We furthermore want to analyze the results of the 4 estimated parameters over time using the lme routine and have thus now 1 row per individual (comprising of the 4 parameters, a time variable and others). Because the 4 parameters are correlated we intend to analyze this multivariate outcome by "flagging" the response by using a dummy coding for the 4 parameters and the time variable as is e.g. described in Doran and Lockwood (2006) p. 223-225 (resulting in 16 rows per individual). Since we want to follow the evolution of the correlation between the 4 parameters over time we would like to make no assumptions on the correlation structure of the errors. We guess we therefore have to use the correlation=corSymm argument. However, the same weighting would apply as in 1) above to the individual and we are therefore not sure again how to define the statistical weights in this case and what this would imply for the error correlation structure. Could you give us a guidance?

Your help is most appreciated and we thank you very much in advance!

Kind regards

Fabian Mollet

Doran, H. C. and Lockwood, J. R. 2006. Fitting value-added models in R. - Journal of Educational and Behavioral Statistics 31: 205-230.

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