R help - Jan 2005 - lme: Variances

Hi R users!

I will try to state my question again. I have longitudinal data and fitted the
following model with lme:

Y = X*beta + U + W(t) + Z

where 

U ~ N(0, nu*I)       I is the identity matrix, so this is the random intercept

W(t)~ N(0, sigma*H)  and H is a matrix which incorporates a Gaussian serial    
                 
                     correlation (covariance) in the offdiagonal elements

Z ~ N(0, tau*J)      the (measurement) error

So lme must have estimated three variance parameters plus the parameter for the
Gaussian correlations. From the output I get, I dont know which is which. The
output was:
> nepal.lme<-lme(ht~sex+died+alive+mage+lit+bf+age+I(age^2),
data=nepal,random=~1|id,correlation=corGaus(corstruct,form=~age|id)
,na.action=na.exclude)
> summary(nepal.lme)
Linear mixed-effects model fit by REML
 Data: nepal 
       AIC    BIC    logLik
  3363.547 3420.7 -1669.774

Random effects:
 Formula: ~1 | id
        (Intercept) Residual
StdDev:    4.240752 1.240242

Correlation Structure: Gaussian spatial correlation
 Formula: ~age | id 
 Parameter estimate(s):
   range 
4.662006 
Fixed effects: ht ~ sex + died + alive + mage + lit + bf + age + I(age^2) 
               Value Std.Error  DF   t-value p-value
(Intercept) 51.07075 2.0274503 674  25.18964  0.0000
sex         -0.54780 0.6210172 191  -0.88210  0.3788
died        -0.01686 0.3915936 191  -0.04306  0.9657
alive       -0.46979 0.2388267 191  -1.96706  0.0506
mage         0.34289 0.0859849 191   3.98785  0.0001
lit          2.62584 1.5123958 191   1.73621  0.0841
bf           0.31873 0.0870432 674   3.66173  0.0003
age          0.86269 0.0198487 674  43.46318  0.0000
I(age^2)    -0.00334 0.0002347 674 -14.24842  0.0000
 Correlation: 
         (Intr) sex    died   alive  mage   lit    bf     age   
sex      -0.419                                                 
died     -0.063 -0.095                                          
alive     0.475  0.041 -0.484                                   
mage     -0.814 -0.035  0.188 -0.780                            
lit      -0.072 -0.099  0.092  0.003  0.059                     
bf       -0.098  0.000  0.002 -0.001  0.008  0.008              
age      -0.168  0.016  0.003 -0.008 -0.018 -0.008  0.250       
I(age^2)  0.146 -0.010 -0.010  0.009 -0.007  0.005 -0.156 -0.917

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-4.22819684 -0.45649041 -0.02996715  0.43379089  2.70363057

Thanks for any help.

Hadassa

Hi Hadassa,
> Random effects:
>  Formula: ~1 | id
>         (Intercept) Residual
> StdDev:    4.240752 1.240242
> 
> Correlation Structure: Gaussian spatial correlation
>  Formula: ~age | id 
>  Parameter estimate(s):
>    range 
> 4.662006 
it looks to me as though you have two variance parameters and the
Gaussian variogram.  I speculate that the model that you've written is
not quite the model that you've fit.  I see no provision for sigma
in your lme statement.  Note p. 230 of Pinheiro and Bates, which
says that "The within-group errors can be standardized to have unit
variance, without changing their correlation structure".  Probably 
sigma is confounded with tau.

If my interpretation is correct, then 

nu = 4.240752 
tau = 1.240242 

and tau also has your sigma in there.  Then the p parameter for your
Gaussian semivariogram is 4.662006.

I hope that this helps,

Andrew

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Andrew Robinson                      Ph: 208 885 7115
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