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Hi All,

Is anyone familiar with negative variance components problem when doing mixed effect models? How do you deal with that? Any recommendations or references are appreciated! Thank you!

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Charlie
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Hello Charlie,

If I understand your question about negative variance component  correctly, then the paragraph below might be of some help..

Often the estimate is very small and estimated just on the other side of zero,  by SAS while using PROC GLIMMIX, in this situation it will nt provide SE of the estime. GLIMMIX model using quadrature method in such situation will result in estimated correlation matrix which is not positive definite. We can avoid this by including a "nobound" option but it is limited to certain methods and we ca not use "nobound " option with the "QUAD" method, however, we can use "nobound" option with method "RSPL"

Most of the times the estimate is not really negative, it is small and has large standard error.
It is possible to get negative variance parameters for instance, in households for outcomes linked to sex, litter weights, twin birth weights etc.

Hope this helps.
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[Tasneem] [Zaihra]
[Assistant Professor]
[Concordia University]
[Montreal]
[QC]
[Canada]
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Hello Tasneem,

This is very helpful. I used to use SAS dealing with mixed effect models, but now I want to figure out how to do it in R. Do you know how to do it in R? The 'lme' function in 'nlme' package seems always bounds the variance components, which will give 0. Thank you.

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Yi Chen
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Original Message:
Sent: 06-13-2012 13:18
From: Tasneem Zaihra
Subject: Negative variance component

Hello Charlie,

If I understand your question about negative variance component  correctly, then the paragraph below might be of some help..

Often the estimate is very small and estimated just on the other side of zero,  by SAS while using PROC GLIMMIX, in this situation it will nt provide SE of the estime. GLIMMIX model using quadrature method in such situation will result in estimated correlation matrix which is not positive definite. We can avoid this by including a "nobound" option but it is limited to certain methods and we ca not use "nobound " option with the "QUAD" method, however, we can use "nobound" option with method "RSPL"

Most of the times the estimate is not really negative, it is small and has large standard error.
It is possible to get negative variance parameters for instance, in households for outcomes linked to sex, litter weights, twin birth weights etc.

Hope this helps.
-------------------------------------------
[Tasneem] [Zaihra]
[Assistant Professor]
[Concordia University]
[Montreal]
[QC]
[Canada]
-------------------------------------------

Hi Charlie,

I don't know what software you are using, but here is how SAS/JMP deals with negative variance components: restricted maximum likelihood estimation or a Bayesian approach depending on the data rather than expected mean squares.

http://www.jmp.com/support/help/Variance_Components.shtml-------------------------------------------
Patrick Spagon
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Hello Patrick,

Thank you for the response. Actually I'm trying to do this in R now. Do you know any package in R using Bayesian approach to address this problem? Thank you.

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Charlie
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Original Message:
Sent: 06-13-2012 13:37
From: Patrick Spagon
Subject: Negative variance component

Hi Charlie,

I don't know what software you are using, but here is how SAS/JMP deals with negative variance components: restricted maximum likelihood estimation or a Bayesian approach depending on the data rather than expected mean squares.

http://www.jmp.com/support/help/Variance_Components.shtml-------------------------------------------
Patrick Spagon
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You might consider subscribing to

     https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

for questions about mixed models in R.

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Jim Baldwin
Station Statistician
US Forest Service
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Original Message:
Sent: 06-13-2012 13:48
From: Yi Chen
Subject: Negative variance component

Hello Patrick,

Thank you for the response. Actually I'm trying to do this in R now. Do you know any package in R using Bayesian approach to address this problem? Thank you.

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Charlie
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You might want to look into the MCMCglmm package in R. I'll second the suggestion to post a question to the R-sig-mixed-models list. That's an excellent resource, where the authors of the LME4 and MCMCglmm packages regularly participate in discussions and answer questions, plus there are many other experts who participate there.

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Steven Pierce
Associate Director
Center for Statistical Training and Consulting
Michigan State University
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Original Message:
Sent: 06-13-2012 13:48
From: Yi Chen
Subject: Negative variance component

Hello Patrick,

Thank you for the response. Actually I'm trying to do this in R now. Do you know any package in R using Bayesian approach to address this problem? Thank you.

-------------------------------------------
Charlie
-------------------------------------------

I don't know how R treats negative variance components, but in the SAS Proc Mixed procedure, the default procedure basically sets negative variance components equal to zero.  To see the variance component go negative in Proc Mixed, one either has to override the default with a "nobound" option, or use a "repeated" statement with "type=cs" in place of the "random" statement.   

Conceptually, I think that a negative variance component is often a problem, but not always a problem, and as a result, I often like to see how negative the variance component gets before I decide what to do about it. 

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Eric Siegel
Biostatistician
Univ of Arkansas for Medical Sciences
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I agree with Eric's statement in second paragraph.   If you have a compound symmetric structure for a repeated measures set-up, you can optionally consider one of two parameter spaces: 1) both variance components positive, or 2) error variance positive and subject-effect variance >= -(error_variance)/n , where n is the number of repeated measures.  The point is that the subject-error variance can actually be negative and still result in a positive-definite variance-covariance matrix for the repeated observations.  Harville discusses this in a TAS paper several years ago. 

But I also think negative variance components suggest there might be a better model to be using (including setting that variance component to be zero, to get started along that line of model fitting).

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[Daniel] [Jeske]
[Professor and Chair]
[Department of Statistics]
[University of California - Riverside]
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Original Message:
Sent: 06-13-2012 14:15
From: Eric Siegel
Subject: Negative variance component

I don't know how R treats negative variance components, but in the SAS Proc Mixed procedure, the default procedure basically sets negative variance components equal to zero.  To see the variance component go negative in Proc Mixed, one either has to override the default with a "nobound" option, or use a "repeated" statement with "type=cs" in place of the "random" statement.   

Conceptually, I think that a negative variance component is often a problem, but not always a problem, and as a result, I often like to see how negative the variance component gets before I decide what to do about it. 

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Eric Siegel
Biostatistician
Univ of Arkansas for Medical Sciences
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A significant negative variance often means that the model should be changed, or examined. Examples include using an unrestricted model when there are restrictions or vice versa. Few examples have been published so your example could be worthy of publication. Jim ------------------------------------------- James Lucas J M Lucas & Associates -------------------------------------------
Original Message: Sent: 06-13-2012 12:59 From: Yi Chen Subject: Negative variance component Hi All, Is anyone familiar with negative variance components problem when doing mixed effect models? How do you deal with that? Any recommendations or references are appreciated! Thank you! ------------------------------------------- Charlie -------------------------------------------

On page 317 of "Analysis of Messy Data: Designed Experiments", 2nd Edition by Milliken and Johnson there is a discussion of one possibility for a negative solution for the variance component.  Sometime it is reasonable for the covariance parameter for the cell variability to be negative because of competition effects within the cells in which case one would re-parameterize and use a Compound symmetry parameter.
George


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George Milliken
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Original Message:
Sent: 06-13-2012 15:25
From: James Lucas
Subject: Negative variance component


A significant negative variance often means that the model should be changed, or examined.
Examples include using an unrestricted model when there are restrictions or vice versa.
Few examples have been published so your example could be worthy of publication.
Jim
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James Lucas
J M Lucas & Associates
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