[S] fixed effects model with unstructure covariance matrix

[ziv shkedy <ziv.shkedy@luc.ac.be>]

Dear Jose and all the S+ users,
I already install the nlme version 3.0. I used the gls function to estimate
the fixed effects
models but i have a problem to define the UNSTRUCTURED covariance matrix.
First I'll describe the dataset that I'm using 
(this dataset is from SAS/STAT Software:Changes and Enhancements through
Release 6.12, 
page 662, Example 18.2.):
Each one of the subjects was measured 4 times,
another covariate in the model is the sex group
(there are no missing values in this specific dataset). 

Example of the data:

    sex resp  time subject(=idnr) 
  1   1 21.0    8   11
  2   1 20.0   10   11
  3   1 21.5   12   11
  4   1 23.0   14   11
  5   1 21.0    8   21
  6   1 21.5   10   21
  7   1 24.0   12   21
  8   1 25.5   14   21
  .   .   .     .   . 
  .   .   .     .   . 
  .   .   .     .   . 
  .   .   .     .   . 
  .   .   .     .   . 
 45   2 26.0    8   12
 46   2 25.0   10   12
 47   2 29.0   12   12
 48   2 31.0   14   12
 49   2 21.5    8   22
 50   2 22.5   10   22
 51   2 23.0   12   22
 52   2 26.5   14   22
  .   .   .     .   . 
  .   .   .     .   . 

I want to fit the following three models:
Model 1 : simple covariance matrix.
Model 2 : random intercept model.
Model 3 : unstructured covariance matrix.

 
I don't have any problems to estimate model 1 and 2 using the following code:

MODEL1 1: Fixed effects model  (Vi=sigma^2*I)
SPlus code:
gls(resp~as.factor(sex)+time:as.factor(sex),data=Gro2,method="ML")

-------------------------------------------------------------------------------
MODEL2 2: Random intercept model (Vi=tau^2*J+sigma^2*I)

SPlus code:
1. hhh <- lme(fixed=resp~as.factor(sex)+time:as.factor(sex),
           random=~1,
           cluster=~idnr,
           est.method=c("ML"),  
           data=Gro2)
OR
2.  hhh <- gls(resp~as.factor(sex)+time:as.factor(sex),data=Gro2,
           method="ML",corCompSymm(form = ~ 1 | idnr))

this model can be estimated in two ways: random intercept model (code 1) or
fixed effects 
model with compound symmetry matrix for the measurement error(code 2)

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

Model 3 : Fixed effect model with unstructured covariance matrix.
          (Vi is a 4*4 matrix with the entries sigma_ij)

Just to make sure that I'm clear, I include first the SAS code for proc MIXED.

SAS code:
proc mixed data=gro2 method=ml covest;
class idnr sex;
model measure = sex time1*sex / s;
repeated / type=un subject=idnr r rcorr;
run;



SPlus code:


hhh <- gls(resp~as.factor(sex)+time:as.factor(sex),data=Gro2,method="ML",
       correlation=corSymm(???????)))

I thought that since the time covariate in my case is "time" and the
grouping level (for the covariance matrix)
is the subjects "idnr" i should use the following code:

correlation=corSymm(form= ~ time|idnr))


But this gives me the folloeing error:
 Error in ## Initialize  objects: Unique values of the covariate  for
"corSymm" objects must be a sequence of consecutive integers
 Dumped

SO HOW CAN I ESTIMATED A FIXED EFFECTS MODEL WITH UNSTRUCTURED CO VARIANCE
MATRIX ?

I also what to mention the motivation in my questions (from today and from
yesterday):
If we think about a model building process then the three model that I
mentioned before are nested models and we can test 
model 3 (as the null model) versus model 2 (or 1) using the LR test. From
this reason, we have to estimate the fixed effects model with 
unstructured covariance matrix. 

thanks, Ziv.



I also include the SAS code for model 1 and 2:

MODEL 1 :
proc mixed data=gro2 method=reml covest;
class idnr sex;
model measure = sex sex*time1/ s;
repeated/ type=simple subject=idnr r rcorr;
run;

MODEL 2 :
proc mixed data=gro2 method=ml ;
class idnr sex;
model measure = sex sex*time1/ s;
random intercept/ type=un subject=idnr g;
run;

OR

proc mixed data=gro2 method=ml ;
class idnr sex;
model measure = sex sex*time1/ s;
repeated/ type=cs subject=idnr r rcorr;
run;























=========================================================
Ziv Shkedy
Biostatistics                   
Center for Statistics           
Limburgs Universitair Centrum
Universitaire Campus, department WNI
B-3590 Diepenbeek, Belgium
Tel: +32-(0)11-26.82.57
e-mail: ziv.shkedy@luc.ac.be 
=========================================================

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