[R-sig-ME] lmer: constraining sigma to 0

[Markus Brauer]

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/




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