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

[Ben Bolker]

On 14-08-14 06:54 AM, Marco Plebani wrote:
> 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

 (Started writing this before Doug's comments, which I agree are [as
usual] thoughtful and sensible but think represent one point of view.)

  For a start, there's a paper that describes the approach in detail:
Chung, Yeojin and Rabe-Hesketh, Sophia and Dorie, Vincent and Gelman,
Andrew and Liu, Jingche. "A Nondegenerate Penalized Likelihood Estimator
for Variance Parameters in Multilevel Models". Psychometrika
doi:10.1007/s11336-013-9328-2

  As for the p-values; I would say that in this context they're not
particularly philosophically coherent but do still represent a rough
measure of strength of evidence ...

  cheers
    Ben Bolker


> 
> ----- 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
> 
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