[R-sig-ME] [R] Comparing variance components

Jarrod Hadfield j.hadfield at ed.ac.uk
Tue Feb 16 21:59:33 CET 2016

Hi Wen,

The question sounds sensible to me, but you can't do what you want to do 
in lmer because it does not allow heterogenous variances for the 
residuals. You can do it in nlme:

model.lme.a<- lme(y~Exp, random=~1|G,  data=my_data)
model.lme.b<- lme(y~Exp, random=~0+Exp|G, 
weights=varIdent(form=~1|Exp),  data=my_data)

or MCMCglmm (or asreml if you have it):

model.mcmc.a<- MCMCglmm(y~Exp, random=~G,  data=my_data)
model.mcmc.b<- MCMCglmm(y~Exp, random=~idh(Exp):G, rcov=~idh(Exp):units, 

The first model assumes common variances for each experiment, the second 
allows the variances to differ. You can comapre model.lme.a and 
model.lme.b using a likelihood ratio test (2 parameters) or you can 
compare the posterior distributions in the Bayesian model.

Note that this assumes that the levels of the random effect differ in 
the two epxeriments (and they have been given separate lables). If there 
is overlap then an additional assumption of model.a is that the random 
effects have a correlation of 1 between the two experiments when they 
are associated with the same factor level.



On 16/02/2016 20:28, Wen Huang wrote:
> Hi Paul,
> Thank you. That is a neat idea. How would you implement that? Could you write an example code on how the model should be fitted? Sorry for my ignorance.
> Thanks,
> Wen
>> On Feb 16, 2016, at 1:18 PM, Thompson,Paul <Paul.Thompson at SanfordHealth.org> wrote:
>> Are you computing two estimates of reliability and wishing to compare them? One possible method is to set both into the same design, treat the design effect (Exp 1, Exp 2) as a fixed effect, and compare them with a standard F test.
>> -----Original Message-----
>> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Wen Huang
>> Sent: Tuesday, February 16, 2016 11:57 AM
>> To: Doran, Harold
>> Cc: r-sig-mixed-models at r-project.org
>> Subject: Re: [R-sig-ME] [R] Comparing variance components
>> Hi Harold,
>> Thank you for your input. I was not very clear. I wanted to compare the sigma2_A’s from the same model fitted to two different data sets. The same for sigma2_e’s. The motivation is when I did the same experiment at two different times, whether the variance due to A (sigma2_A) is bigger at one time versus another. The same for sigma2_e, whether the residual variance is bigger for one experiment versus another.
>> Thanks,
>> Wen
>>> On Feb 16, 2016, at 12:40 PM, Doran, Harold <HDoran at air.org> wrote:
>>> (adding R mixed group). You actually do not want to do this test, and there is no "shrinkage" here on these variances. First, there are conditional variances and marginal variances in the mixed model. What you are have below as "A" is the marginal variances of the random effects and there is no shrinkage on these, per se.
>>> The conditional means of the random effects have shrinkage and each conditional mean (or BLUP) has a conditional variance.
>>> Now, it seems very odd to want to compare the variance between A and then what you have as sigma2_e, which is presumably the residual variance. These are variances of two completely different things, so a test comparing them seems strange, though I suppose some theoretical reason could exists justifying it, I cannot imagine one though.
>>> -----Original Message-----
>>> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Wen
>>> Huang
>>> Sent: Tuesday, February 16, 2016 10:57 AM
>>> To: r-help at r-project.org
>>> Subject: [R] Comparing variance components
>>> Dear R-help members,
>>> Say I have two data sets collected at different times with the same
>>> design. I fit a mixed model using in R using lmer
>>> lmer(y ~ (1|A))
>>> to these data sets and get two estimates of sigma2_A and sigma2_e
>>> What would be a good way to compare sigma2_A and sigma2_e for these two data sets and obtain a P value for the hypothesis that sigma2_A1 = sigma2_A2? There is obvious shrinkage on these estimates, should I be worried about the differential levels of shrinkage on these estimates and how to account for that?
>>> Thank you for your thoughts and inputs!
>>> 	[[alternative HTML version deleted]]
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