[R-sig-ME] Problematic correlations between random effects

[David Duffy]

On Thu, 23 Feb 2012, Leite,Walter wrote:

> Folks,
>
> I fitted a model with several random effects to data with a 
> cross-classification of students and schools using lmer. Two random 
> effects have correlation of -1 and others near 1, as shown below. I 
> thought that this would only occur if any random effects were not 
> necessary in the model, but I built this model adding the random effects 
> one at a time and comparing the fit with BIC and AIC. Also, none of the 
> variances are very small. Could someone advise me on why these 
> correlations occurred and ways I can solve this problem?
>
> Random effects:
> Groups    Name             Variance  Std.Dev. Corr
> CHILDID   (Intercept)      333.63787 18.26576
>           time.period        7.99838  2.82814 -1.000
>           I(time.period^2)  11.16830  3.34190 -0.514  0.514
>           I(time.period^3)   0.31869  0.56453 -0.189  0.189  0.938
> School_ID (Intercept)       87.59255  9.35909
>           time.period       33.30370  5.77094  0.093
>           I(time.period^2)   1.48008  1.21659 -0.171  0.960
> Residual                    39.94649  6.32032
> Number of obs: 11960, groups: CHILDID, 2990; School_ID, 996

Have you centred time.period?  My simple minded understanding is that 
polynomial terms like that will always be highly correlated unless you 
orthogonalize them, but the LR based criteria will still guide you 
correctly.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v