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

[Aurore Paligot]

Thank you very much, Ben, for your answer and the useful links. Blme sounds like a great solution, I will retry with this package.
Best regards, 
Aurore

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.




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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