Re: [R] How to assess significance of random effect in lme4

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Thu 18 Aug 2005 - 22:26:04 EST

Hi, Harold: Thanks for the clarification. I thought I had read the original post. Obviously, I had misread it. Thanks again. spencer graves

Doran, Harold wrote:

> Yes, it is a different issue. ranef() extracts the empirical Bayes
> estimates, which are the empirical posterior modes. The bVar slot holds
> the corresponding posterior variances of these modes.
>
> Technically, (according to D. Bates) the values in the bVar slot are the
> the diagonal elements of
> (Z'Z+\Omega)^{-1}.
>
> The original post was asking how to test and compare a specific random
> effect, not a general assessment of how much information is provided by
> the data via LRT.
>
> Shige asked how to test whether a specific EB estimate is different than
> some other value.
> LRT doesn't answer this question, but the values in the bVar slot do.
>
>
> -----Original Message-----
> From: Spencer Graves [mailto:spencer.graves@pdf.com]
> Sent: Wed 8/17/2005 10:08 PM
> To: Doran, Harold
> Cc: Shige Song; r-help@stat.math.ethz.ch
> Subject: Re: [R] How to assess significance of random effect in lme4
>
> Is there some reason you are NOT using "anova", as in "Examples"
> section of "?lmer"?
>
> Permit me to summarize what I know about this, and I'll be
> pleased if
> someone else who thinks they know different would kindly enlighten me
> and others who might otherwise be misled if anything I say is
> inconsistent with the best literature available at the moment:
>
> 1. Doug Bates in his PhD dissertation and later in his book
> with Don
> Watts (1988) Nonlinear Regression Analysis and Its Applications (Wiley)
> split approximation errors in nonlinear least squares into "intrinsic
> curvature" and "parameter effects curvature". He quantified these two
> problems in the context of roughly three dozen published examples, if my
> memory is correct, and found that in not quite all cases, the parameter
> effects were at least an order of magnitude greater than the intrinsic
> curvature.
>
> 2. In nonnormal situations, maximum likelihood is subject to more
> approximation error -- intrinsic curvature -- than "simple" nonlinear
> least squares. However, I would expect this comparison to still be
> fairly accurate, even if the differences may not be quite as stark.
>
> 3. The traditional use of "standard errors" to judge statistical
> significance is subject to both intrinsic and parameter effects errors,
> while likelihood ratio procedures such as anova are subject only to the
> intrinsic curvature (assuming there are no substantive problems with
> nonconvergence). Consequently, to judge statistical significance of an
> effect, anova is usually substantially better than the so-called Wald
> procedure using approximate standard errors, and is almost never worse.
> If anyone knows of a case where this is NOT true, I'd like to know.
>
> 4. With parameters at a boundary as with variance components, the
> best procedure seems to double the p-value from a nested anova (unless
> the reported p-value is already large). This is because the
> 2*log(likelihood ratio) in such cases is roughly a 50-50 mixture of 0
> and chi-square(1) [if testing only 1 variance component parameter].
> This is supported by a substantial amount of research, including
> simulations discussed in a chapter in Pinheiro and Bates (2000)
> Mixed-Effects Models in S and S-Plus (Springer). The may be more
> accurate procedures available in the literature, but none so simple as
> this as far as I know.
>
> Comments?
> spencer graves
> p.s. It looks like fm@bVars is a list containing vectors of length 29
> and 6 in your example. I don't know what they are, but I don't see how
> they can be standard errors in the usual sense.
>
> Doran, Harold wrote:
>
> > These are the posterior variances of the random effects (I think more
> > properly termed "empirical" posteriors). Your model apparently includes
> > three levels of random variation (commu, bcohort, residual). The first
> > are the variances associated with your commu random effect and the
> > second are the variances associated with the bcohort random effect.
> >
> > Accessing either one would require
> >
> > fm@bVar$commu or fm@bVar$bcohort
> >
> > Obviously, replace "fm" with the name of your fitted model.
> >
> > -----Original Message-----
> > From: r-help-bounces@stat.math.ethz.ch
> > [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Shige Song
> > Sent: Wednesday, August 17, 2005 7:50 AM
> > To: r-help@stat.math.ethz.ch
> > Subject: Re: [R] How to assess significance of random effect in lme4
> >

> > Hi Harold,
> >
> > Thanks for the reply. I looked at my outputs using str() as you
> > suggested, here is the part you mentioned:
> >
> > ..@ bVar :List of 2
> > .. ..$ commu : num [1, 1, 1:29] 5e-10 5e-10 5e-10 5e-10 5e-10 ...
> > .. ..$ bcohort: num [1, 1, 1:6] 1.05e-05 7.45e-06 6.53e-06 8.25e-06
> > 7.11e-06 ...
> >
> > where commu and bcohort are the two second-level units. Are these
> > standard errors? Why the second vector contains a series of different
> > numbers?
> >
> > Thanks!
> >
> > Shige
> >
> > On 8/17/05, Doran, Harold <HDoran@air.org> wrote:
> >
> >>
> >>
> >>You can extract the posterior variance of the random effect from the
> >>bVar slot of the fitted lmer model. It is not a hidden option, but a
> >>part of the fitted model. It just doesn't show up when you use
> >
> > summary().
> >
> >>
> >> Look at the structure of your object to see what is available using
> >
> > str().
> >
> >>
> >> However, your comment below seems to imply that it is incorrect for
> >>lmer to report SDs instead of the standard error, which is not true.
> >>That is a quantity of direct interest.
> >>
> >> Other multilevel programs report the same exact statistics (for the
> >>most part). For instance, HLM reports the variances as well. If you
> >>want the posterior variance of an HLM model you need to extract it.
> >>
> >>
> >>
> >> -----Original Message-----
> >> From: r-help-bounces@stat.math.ethz.ch on behalf of
> >>Shige Song
> >> Sent: Wed 8/17/2005 6:30 AM
> >> To: r-help@stat.math.ethz.ch
> >> Cc:
> >> Subject: [R] How to assess significance of random effect in
> >
> > lme4
> >
> >>
> >> Dear All,
> >>
> >> With kind help from several friends on the list, I am getting close.
> >> Now here are something interesting I just realized: for random
> >>effects, lmer reports standard deviation instead of standard error! Is
> >
> >
> >>there a hidden option that tells lmer to report standard error of
> >>random effects, like most other multilevel or mixed modeling software,
> >
> >
> >>so that we can say something like "randome effect for xxx is
> >>significant, while randome effect for xxx is not significant"? Thanks!
> >>
> >> Best,
> >> Shige
> >>
> >> ______________________________________________
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> >> PLEASE do read the posting guide!
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> >>
> >>
> >>
> >>
> >>
> >
> >
> > ______________________________________________
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>
> --
> Spencer Graves, PhD
> Senior Development Engineer
> PDF Solutions, Inc.
> 333 West San Carlos Street Suite 700
> San Jose, CA 95110, USA
>
> spencer.graves@pdf.com
> www.pdf.com <http://www.pdf.com>
> Tel: 408-938-4420
> Fax: 408-280-7915
>
>

-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves@pdf.com
www.pdf.com <http://www.pdf.com>
Tel:  408-938-4420
Fax: 408-280-7915

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Received on Thu Aug 18 22:30:36 2005

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