Dear all,
   
  I noticed the following in the call of lme using msVerbose.
   
  fm1 <- lme(distance ~ age, data = Orthodont, control = lmeControl(msVerbose=T))
   
    9      318.073: -0.567886 0.152479  1.98021
 10      318.073: -0.567191 0.152472  1.98009
 11      318.073: -0.567208 0.152473  1.98010

   
  fm2 <- lme(distance ~ age, random =~age, data = Orthodont, lmeControl(msVerbose=T))
   
    7      318.073: -0.342484  1.75530  4.44650
  8      318.073: -0.342507  1.75539  4.44614
  9      318.073: -0.342497  1.75539  4.44614

   
  The two model are equivalent and give the same estimates. However, the optimal parameters in the profiled log-likelihood are not the same? why?
   
  As I usually thought, the parameters optimised in the profiled likelihood are the log of the precision matrix. The latter can be  derived  as a Cholesky factorization of  the product between the residuals variance and the inverse of the random effects covariance. When I check that it's not the case for model fm1 even if it's equivalent to model fm2.
   
   log(chol(((summary(fm1)$sigma)^2)*solve( matrix(getVarCov(fm1), nrow=2))))
   
                 [,1]            [,2]
[1,]     -0.3424971     1.492037
[2,]      -Inf               1.755388

  log(chol(((summary(fm2)$sigma)^2)*solve( matrix(getVarCov(fm2), nrow=2))))

   
                 [,1]            [,2]
[1,]     -0.3424971     1.492037
[2,]      -Inf               1.755388

   
  In the two mdels, this terms are equals to the optimized parameters in fm2 not in fm1. I am missing something I suppose.
   
  Bests,
   
  Bernard

             
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