[R-sig-ME] Random effect variance = zero

[Marco Plebani]

Dear list members,

Package blme has been suggested for fixing issues with random effect variance = zero in other occasions, but I do not understand the rationale behind it. What does blme that lme4 does not? In which way do the two approaches differ? In particular:
- what is the prior information that blme is using, and
- how comes that blme still estimates parameter values and assign p-values to them? According to my (very limited) knowledge of bayesian stats the outcome of the analysis should be an updated distribution of the possible parameter values.

The available documentation about blme is limited and/or I could not find it. I realize that my question on blme hides another, much broader, on how bayesian stats work; regarding the latter, a suggestion of a good, practice-oriented reference book would be appreciated.

Thank you in advance,

Marco

-----
Marco Plebani, PhD candidate (Ecology) at the University of Zurich
Institute of Evolutionary Biology and Environmental Studies
http://www.ieu.uzh.ch/staff/phd/plebani.html

On 13/ago/2014, at 12:00, r-sig-mixed-models-request at r-project.org wrote:

> Date: Tue, 12 Aug 2014 12:35:10 -0400
> Subject: Re: [R-sig-ME] Random effect variance = zero
> From: bbolker at gmail.com
> To: aurorepaligot at hotmail.com
> CC: r-sig-mixed-models at r-project.org
> 
> 
> Short answer: yes, very common outcome, especially with small numbers of random effects groups (e.g. <5).  See http://glmm.wikidot.com/faq ; blme package for 'regularizing' fits so this doesn't happen (at the expense of changing the statistical model slightly); http://rpubs.com/bbolker/4187 .
> 
> 
> 
> On Tue, Aug 12, 2014 at 12:05 PM, Aurore Paligot <aurorepaligot at hotmail.com> wrote:
> 
> Hello Everybody, I am new at using mixed models, and I would like some advice about some results that I obtained and that seem counter-intuitive to me.  As an output of a test, I obtainded a variance of zero for a random factor.
> 
> […] How is it possible?  Can it be considered as a reasonable output?
> 
> I found this information about the variance estimates of zero. Could this explanation apply to my study?
> 
> "It is possible to end up with a school variance estimate of zero. This fact often puzzles the researcher since each school will most certainly not have the same mean test result. An estimated among-school variance being zero, however, does not mean that each school has the same mean, but rather that the clustering of the students within schools does not help explain any of the overall variability present in test results. In this case, test results of students can be considered as all independent of each other regardless if they are from the same school or not. "( http://www.cscu.cornell.edu/news/statnews/stnews69.pdf )
> 
> If not, where could the problem come from? Is the formula that I used correct? Is a mixed-model appropriate for this type of question?
> 
> I would really appreciate some clarification if someone already faced this type of problem !
> 
> Best regards,
> 
> Aurore