[R-sig-ME] Correlation of -1: is it a problem?

[Douglas Bates]

On Fri, Mar 26, 2010 at 1:18 PM, Eric Castet
<Eric.Castet at incm.cnrs-mrs.fr> wrote:
> Dear all,
>
> I would be grateful if you could help me with the following question
> using lmer()
> I want to test the effect of a categorical factor with two levels
> (called 'couleurs')
> The only random factor is 'nom'.
>
> I first start with all random effects (I only report the lines for the
> random effects):
> Linear mixed model fit by maximum likelihood
> Formula: lRT ~ couleurs + (1 + couleurs | nom)
> Random effects:
>  Groups          Name            Variance  Std.Dev. Corr
>  nom              (Intercept)     0.1376693 0.371038
>                      couleurs1       0.0030358 0.055098 *-1.000 *
>  Residual                             0.5118424 0.715432
> Number of obs: 7927, groups: nom, 10
>
>
> Then, I remove the random effect of 'couleurs'  with the following result:
>
> Linear mixed model fit by maximum likelihood
> Formula: lRT ~ couleurs + (1 | nom)
>   Data: jb
>
> Random effects:
>  Groups       Name            Variance Std.Dev.
>  nom          (Intercept)     0.11768  0.34304
>  Residual                         0.51263  0.71598
> Number of obs: 7927, groups: nom, 10
>
> I then compare the two models and see that I should go with the first
> model Df=6:
>  > anova (jb.lmer1, jb.lmer2)
> Data: jb
> Models:
> jb.lmer2: lRT ~ couleurs + (1 | nom)
> jb.lmer1: lRT ~ couleurs + (1 + couleurs | nom)
>         Df   AIC   BIC  logLik  Chisq Chi Df Pr(>Chisq)
> jb.lmer2  4 17259 17287 -8625.4
> jb.lmer1  6 17251 17293 -8619.4 12.078      2   0.002384 **

> My questions are the following:

> a/ is it really a statistical (or numerical) problem to have a -1
> correlation in the model that I should keep?

Yes, it is.  The fitted model is has a singular variance-covariance
matrix for the random effects and that is not good.  In fact, it is no
longer a linear mixed model.

> b/ is it possible to remove the correlation between Intercept and
> Couleurs, as I would do if Couleurs were not a categorical factor?

I would fit another model of

IRT ~ couleurs + (1|nom:couleurs) + (1|nom)

and see how that works.  This model is, in some sense, intermediate to
the models that you have fit above.

>
> Thanks in advance,
>
> Eric Castet
>
>
>
>
> --
>
> Eric Castet
>
> Institut de Neurosciences Cognitives de la Méditerranée -- INCM CNRS
>
> 31 chemin Joseph Aiguier
>
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>
> tel : (+33)(0)4-91-16-43-34
>
> fax : (+33) (0)4-91-16-44-98
>
> UMR 6193 du CNRS
>
> Université Aix-Marseille II
>
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>
> http://www.incm.cnrs-mrs.fr/pperso/ecastet.php
>
>
>
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