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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