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

[Dean Castillo]

Hi Jarrod,

I have been trying to test a similar hypothesis for a while with only
limited success, so I wanted to thank you for your answer to Wen's
question. I did have a few additional questions of clarification, some
specific to my own data analysis.

For model.mcmc.a I think it is pretty straightforward to compare the
posterior distributions. For model.mcmc.b, now that you explicitly modeled
heterogenous variances for the residuals is it more informative to examine
the IC correlation for G for each Exp rather than the variances themselves?

For my specific problem I have binomial data. I have been modeling the data
as proportions (bounded by 0-1 but can logit or arcsinsqrt transform) as
well as modeling it using "multinomial2" on the raw data.

The issue I am running into is that the variance of G for one of the
experimental blocks is very close to the boundary condition, while the
other is larger, when modeled as a proportion, and the HPD are very wide. I
have been using inv-gamma priors and will play around with the parameter
expanded priors as suggested in your course notes.

For the multinomial2 model should the priors for the variance be the same?
The posterior means are not as close to the boundary condition (Exp1:G=0.8,
Exp2:G=0.3) but the HPD are still very wide (1e-17,1.13) for Exp2:G.

Any help is greatly appreciated

Dean



> Date: Tue, 16 Feb 2016 20:59:33 +0000
> From: Jarrod Hadfield <j.hadfield at ed.ac.uk>
> To: Wen Huang <whuang.ustc at gmail.com>,  "Thompson,Paul"
>         <Paul.Thompson at SanfordHealth.org>
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] [R] Comparing variance components
> Message-ID: <56C38DB5.2010709 at ed.ac.uk>
> Content-Type: text/plain; charset=utf-8; format=flowed
>
> 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,
> data=my_data)
>
> 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.
>
> Cheers,
>
> Jarrod
>
>
>
> 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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