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

[Ben Bolker]

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.
>
> Data
> I am looking at the distance between the hands in symmetrical signs of a
> sign language. This is my dependent  variable. I have four signers
> (speakers), recorded in four different contexts. I have 320 observations in
> total : 20 for each signer in each context.
> Research question
> I want to see whether there is a relationship between the distance between
> the hands and the context of use (more or less formal). Context is defined
> here as a fixed factor with four levels : C1, C2, C3, C4.
> Formula
> Context.model = lmer (Distance ~ Context + (1|Signer), data=context)
> Results
> For the random factor "Signer", the variance and standard deviation are
> both equal to zero:
> Linear mixed model fit by REML ['lmerMod']Formula: Ecart ~ Contexte + (1 |
> Locuteur)   Data: context
> REML criterion at convergence: 2986.4
> Scaled residuals:     Min      1Q  Median      3Q     Max -1.6085 -0.5709
> -0.1486  0.2404  7.0084
> Random effects: Groups   Name        Variance Std.Dev. Locuteur
> (Intercept)   0.0     0.00    Residual                       725.7    26.94
>   Number of obs: 319, groups:  Locuteur, 4
> Fixed effects:            Estimate Std. Error t value(Intercept)  4.10312
>    3.01187   1.362ContexteC2  14.60662    4.27288   3.418ContexteC3
>  -0.09983    4.27288  -0.023ContexteC4  23.22922    4.24626   5.471
> Correlation of Fixed Effects:           (Intr) CntxC2 CntxC3ContexteC2
> -0.705              ContexteC3 -0.705  0.497       ContexteC4 -0.709  0.500
>  0.500
> Questions
> 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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>
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