[R-sig-ME] Meaning of perfect correlation between by-intercept and by-slope adjustments

[Petar Milin]

On 13/05/11 22:00, Douglas Bates wrote:
> On Fri, May 13, 2011 at 12:35 PM, Petar Milin<pmilin at ff.uns.ac.rs>  wrote:
>> Hello! Simplified model that I have is:
>> lmer(Y ~ F1 + F2 + C1 + (1+F1|participants) + (1|items))
>> F1 and F2 are categorical predictors (factors) and C1 is a covariable
>> (continuous predictor). F1 has five levels.
>> By-participant adjustments for F1 are justified (likelihood ratio test is
>> highly significant). However, what puzzles me is perfect correlation between
>> two levels of F1. Others are quite high, but not perfect. I wonder what this
>> means, exactly? Is there some "lack of information" which leads to problems
>> in estimating variances?
> I think of the estimation criterion for mixed models (the REML
> criterion or the deviance) as being like a smoothing criterion that
> seeks to balance complexity of the model versus fidelity to the data.
> It happens that models in which the variance covariance matrix of the
> random effects is singular or nearly singular are considered to have
> low complexity so the criterion will push the optimization to that
> extreme when doing so does not introduce substantially worse fits.
>
> One way around this is to avoid fitting models with vector-valued
> random effects and, instead, use two terms with simple scalar random
> effects, as in
>
> lmer(Y ~ F1 + F2 + C1 + (1|participants) + (1|F1:participants) + (1|items))
I am always hesitant to go for scalar version. As far as I understand, 
this implies homoscedasticity across levels of F1, but correct me if I 
am wrong. In my model, I am not sure if that would be correct.

Best,
Petar