Singular estimated var-cov

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.