lmer: constraining sigma to 0

Dear colleague,

I came across a website/forum in which you talked about
constraining the residual variance to zero (in LMEMs):

http://permalink.gmane.org/gmane.comp.lang.r.lme4.devel/11418

I am aware that you suggested to use blmer. Has there been any 
development since 2013? Is there a way to fix sigma EXACTLY to zero
now?

Here is the problem. Like you, I teach statistics and linear 
mixed-effects models. My students and I frequently use lmer to
analyze data with one or multiple sources of non-independence.
However, I run into problems with designs that contain only
dichotomous within-subject variables and only one data point per
cell of the design per subject. In these designs, the residuals are
zero (the level-1 models perfectly fit the data). I understand that
technically, such a linear mixed-effects models are not
identifiable. They would be identifiable, however, if I could fix
the parameter for the variance of the residuals to zero.

I can, of course, transform my data into wide format and analyze
them with a GLM procedure (e.g., lm) but it seems bizarre to have
to go through the tedious data restructuring process (dcast ...)
and use different commands for a certain type of design that is in
fact quite similar to other designs that can easily be analyzed
with lmer.

I tried a number of things (e.g., not including any random slopes,
not including the random slope for the highest order interaction
effect), but none of them gave me the ?right? values for the
inferential statistics. Take a 2 x 2 within-subjects ANOVA with one
data point per cell of the design from each participant. By
transforming the data into wide format and using a standard GLM
procedure I can obtain the ?right? F- and p-values. I have not
found a way to obtain the same values with the data in long format
(i.e., four lines per participant) and using lmer. It doesn?t
matter which random effects structure I specify ? I am not getting
the ?right? F- and p-values.

The only trick I have found in lmer is to suppress the error
message with control=lmerControl(check.nobs.vs.nRE="ignore"). But
suppressing the error message is not the same as constraining sigma
to be zero.

Do you know how to fix the parameter for the variance of the
residuals to zero?

Thanks a lot for your insight. Best wishes,

? Markus



----------------------------------------------- Markus Brauer 
Professor Department of Psychology University of Wisconsin -
Madison 1202 West Johnson St. Madison, WI 53706-1611 USA Tel.
+1-608-890-3313 Cell +1-608-692-3468 Fax  +1-608-262-4029 Office
417 Web Page: http://psych.wisc.edu/brauer/BrauerLab/