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

[Rubén Roa]

-----Mensaje original-----
De: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] En nombre de Eric Castet
Enviado el: lunes, 29 de marzo de 2010 19:45
Para: Douglas Bates
CC: r-sig-mixed-models at r-project.org
Asunto: Re: [R-sig-ME] Correlation of -1: is it a problem?

Dear Doug,

Thanks for your reply.

I've done as you suggested (your point b/), i.e. I've fit another model that considers 'couleurs' within 'nom'
However, after running anova() (likelihood ratio test), I find that I should keep the initial model that contains the -1 correlation:

 > anova (jb.lmer1, jb.lmer2)
Data: jb
Models:
jb.lmer2: lRT ~ couleurs + (1 | nom) + (1 | nom:couleurs)
jb.lmer1: lRT ~ couleurs + (1 + couleurs | nom)
          Df   AIC   BIC  logLik  Chisq Chi Df Pr(>Chisq)
jb.lmer2  5 17260 17295 -8625.2
jb.lmer1  6 17251 17293 -8619.4 11.584      1  0.0006654 ***

So, the question is now:

a/ How can I justify to refuse the initial model that contains the -1 correlation?

b/ And a parallel question is: what is wrong with the -1 correlation? Is it because it is exactly -1 ? Would it still be a problem if it were -0.99 ?

c/ Ultimately, how can I report what appears to me as an important
result: namely the high correlation between the intercept and the 'couleurs' effect for each subject?

--------

When I see a correlation very close to 1 or -1 between parameter estimates (mostly in nonlinear models, because that is my main area) I start to think of ways to re-parameterize the model, i.e. some change in the algebraic structure that introduces different parameters, because a nearly-perfect correlation is telling me that one of the highly correlated parameter estimates is redundant: the sample does not have any more information about one parameter than it has about the other.
Probably the perfect correlation is telling you that you don't need a statistical test to tell what you want to tell.

HTH

Rubén


____________________________________________________________________________________ 

Dr. Rubén Roa-Ureta
AZTI - Tecnalia / Marine Research Unit
Txatxarramendi Ugartea z/g
48395 Sukarrieta (Bizkaia)
SPAIN