[R] Specific structure of variance-covariance matrix in the lme function for a linear mixed effect models

[Caroline Bazzoli]

Dear all,

We are using lme function to estimate a mixed effect model.
The data are obtained from the following experience:

15 subjects were required to press maximally ledges with four fingers 
and magnitudes of the 4 fingers are measured simultaneously for three 
different positions.
Three repetitions of each measure are made. The data set is thus 
composed of 540 measures.

We have fitted this data with the following model :

F_idkj = mu + beta_d + alpha_k + interaction terms + random effect terms 
+ error terms
with i=subject (i=1,..,15), d=finger (d=1,...,4), k=position 
(k=1,...,3), j=repeated measure (j=1,..3)

We have tested this model with different structure for the 
variance-covariance matrix of the error model using the options "weight" 
and "correlation" in the lme function.
A specific case was to introduce dependence between fingers (correlation 
among the errors) which can be different by position.
This step consisted to implement a block-diagonal matrix (one block 
corresponding to one position). To do that, we used the following command:


//fitM<lme(F~finger*position,random=~1|Subject/position,data=DataALL,method="ML",correlation=corSymm(form=~1|Subject/position/Repet))
//
//summary(fitM)
//
//Linear mixed-effects model fit by maximum likelihood
// Data: DataALL //
//      AIC BIC    logLik//
//  4244.71 4334.833 -2101.355//
//
//Random effects://
// Formula: ~1 | Subject//
//        (Intercept)//
//StdDev:  0.00138398//
//
// Formula: ~1 | position %in% Subject//
//        (Intercept) Residual//
//StdDev:    5.549804 11.36901//
//
//Correlation Structure: General//
// Formula: ~1 | Subject/position/Repet //
// Parameter estimate(s)://
// Correlation: //
//  1      2      3 //
//2  0.040 //
//3 -0.261 -0.007 //
//4 -0.356 -0.181  0.081//
//Fixed effects: F ~ finger * position //
// Value Std.Error  DF   t-value p-value//
//(Intercept)       23.000000  2.244465 486 10.247432 0.0000//
//fingerM -0.600000  2.374891 486 -0.252643 0.8007//
//fingerR -1.622222  2.721607 486 -0.596053 0.5514//
//fingerL 0.000000  2.822485 486  0.000000 1.0000//
//positionFlexP3         0.000000 3.174153  28  0.000000 1.0000//
//positionExtP1         -0.555556 3.174153  28 -0.175025 0.8623//
//fingerM:positionFlexP3 -0.288889  3.358603 486 -0.086015 0.9315//
//fingerR:positionFlexP3  1.622222  3.848934 486  0.421473 0.6736//
//fingerL:positionFlexP3  0.000000  3.991596 486  0.000000 1.0000//
//fingerM:positionExtP1   0.622222  3.358603 486  0.185262 0.8531//
//fingerR:positionExtP1   1.977778  3.848934 486  0.513851 0.6076//
//fingerL:positionExtP1  -0.533333  3.991596 486 -0.133614 0.8938//
// Correlation: //
// (Intr) fingerM fingerR fingerL stFlP3 stExP1 dM:FP3 dR:FP3//
//fingerM -0.529 //
//fingerR -0.606 0.551 //
//fingerL -0.629  0.497 0.649 //
//positionFlexP3        -0.707 0.374  0.429 0.445 //
//positionExtP1         -0.707 0.374  0.429  0.445 0.500 //
//fingerM:positionFlexP3  0.374 -0.707 -0.390 -0.352 -0.529 -0.265 //
//fingerR:positionFlexP3  0.429 -0.390 -0.707 -0.459 -0.606 -0.303 0.551 //
//fingerL:positionFlexP3  0.445 -0.352 -0.459 -0.707 -0.629 -0.314 
0.497  0.649//
//fingerM:positionExtP1   0.374 -0.707 -0.390 -0.352 -0.265 -0.529  
0.500  0.276//
//fingerR:positionExtP1   0.429 -0.390 -0.707 -0.459 -0.303 -0.606  
0.276  0.500//
//fingerL:positionExtP1   0.445 -0.352 -0.459 -0.707 -0.314 -0.629  
0.249  0.325//
// dL:FP3 dM:EP1 dR:EP1//
//fingerM //
//fingerR //
//fingerL //
//positionFlexP3 //
//positionExtP1 //
//fingerM:positionFlexP3 //
//fingerR:positionFlexP3 //
//fingerL:positionFlexP3 //
//fingerM:positionExtP1   0.249 //
//fingerR:positionExtP1   0.325  0.551 //
//fingerL:positionExtP1   0.500  0.497  0.649//
//
//Standardized Within-Group Residuals://
// Min Q1 Med          Q3 Max //
//-2.61928606 -0.73819468  0.00057926  0.78983154 2.16414994 //
//
//Number of Observations: 540//
//Number of Groups: //
//          Subject position %in% Subject //
// 15 45 /



Nevertheless, this output displays identical blocks. It means that the 
dependence between fingers is the same for each position.
We would like to test a model with different blocks to model different 
position dependence.

Any help with this is greatly appreciated.

Thanks in advanced for yours attention!


Caroline bazzoli

-- 
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