# [R] lme output

From: Marc Bernard <bernarduse1_at_yahoo.fr>
Date: Wed, 5 Dec 2007 11:34:18 +0100 (CET)

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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