I am sure the master (DB) is right in his comments But I wonder if you have
tried something easier. I did not get your data eitehr but you said
something about high correlations. Is your time variable centerd around
zero? This will make no difference to your fitted values and likelihood if
the models have converged to the ML solution, but centering will
sometimes overcome fitting problems.
If the variance covariance matrix at the solution really is singular then
obviously it won't help. If your fit gives you random effects than I would
suggest extracting them and plotting the equivalent lines, so you can see
what is going on. The most likley scenario from what you describe is that
your lines all pass through a common point for some choice of X value. You
could probably work this out from the fitted variance covariance matrix, but
I find the fitted lines help me to see what is going on better than the
algebra.
Gillian Raab, Edinburgh
On 13/10/2008, Douglas Bates wrote:
>
> On Thu, Oct 9, 2008 at 7:27 AM, wrote:
> > Dear list members,
>
> > I try to fit a model (using lmer) to data recorded at 4 time points
> > (days). Each such time series corresponds to a distinct subject. There
> are
> > two treatment groups. There is also a patient-level covariate ("o" or
> > "b"). I am attaching the data frame (as a binary R object) and the R
> > script that loads the data frame and fits the models.
>
> I regret it has taken so long for you to get a response to your
> question but I don't think that we can try the fit because you didn't
> attach the data frame or the script - or at least they didn't make it
> through the mail list software if you did include them.
>
> > The questions are 1) whether the drug effect is influenced by the
> > covariate, and 2) whether there is a temporal trend in drug effect over
> > days.
>
> > The problem is that according LMER the covariance matrix for this problem
> > is singular, and as a result the fitted models do not capture the
> > variability of slopes that is seen in the data. Apparently there is a
> > strong correlation between some parameters that leads to this singularity
> > ? Perhaps I misspecified the model for LMER (and LME) ?
>
> It is possible for the estimated covariance matrix to be singular even
> when there is significant variability in both the slope and the
> intercept. An example of that is enclosed.
>
> We can think of fitting mixed models as a smoothing problem where we
> need to balance fidelity to the data against the complexity of the
> model. The model complexity happens to be measured by a determinant
> and a model with a singular covariance for the random effects has a
> small value of this determinant. If there is not a correspondingly
> large loss of fidelity to the data caused by the singular covariance
> matrix then the estimates will be singular.
>
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>
>
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Gillian M Raab
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