[R-sig-ME] Negative estimates of variance component

[Chris Brien]

Dear all,

Doug, thanks for the information that negative estimates are not possible with lme4 and nlme.

As for the questions from others about why would you want to do it, there are a number of reasons.

Of course, variance components must be positive. However, one reason, given by Littel et al in  SAS for Mixed Models, to allow negative estimates is that it controls Type I error better and in certain circumstance may give better power. This is essentially related to the issue of pooling non-significant error terms. In SAS MIXED there is an option to allow negative estimates. 

Another reason is that variance components might be interpreted as components of excess variation or even excess covariance. Then negative values indicate less covariance between than within groups, as Jerome explained. However, as suggested in the "Heywood case" scenario, reasons for negative estimates need to be investigated to make sure that it really is negative covariance. As for fitting using structured covariance matrices as suggested by Ben, this is a nice way to go about it but requires that the software has this capability. Lme4 does not have it and nlme is not good at fitting crossed factors - a gotcha' situation.

A third reason is that in order to approximate a randomization analysis, one needs to allow for negative estimates. I reiterate that here I am thinking of variance components as surrogates for components of excess covariance.

So, I do not agree that it is in the category of "consistency with older method-of-moments estimates". The issue is more that there is no coherent way to specify the types of models of which I am thinking in current software packages.

Cheers,

  Chris


-----Original Message-----
From: Ben Bolker [mailto:bbolker at gmail.com] 
Sent: Friday, 30 July 2010 7:02 PM
To: jerome.goudet at unil.ch
Cc: Chris Brien; r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Negative estimates of variance component

  I claim that this is in the category of "consistency with older
method-of-moments estimates" ... I know that population geneticists
still like to think in terms of variance components, but wouldn't one
ideally want to deal with the negative correlation built into the
system by estimating it more or less directly (i.e. via a structured
variance-covariance model that has nonnegative variances but could
have negative covariances) rather than by estimating a negative
variance component?

  Ben Bolker (not a population geneticist so possibly missing the point)

On Fri, Jul 30, 2010 at 12:39 PM, Jerome Goudet <jerome.goudet at unil.ch> wrote:
> Hi all,
>
> Here is an example: genes are nested in individuals, themselves nested in
> populations.  If individuals avoid mating with relatives, then the variance
> component of allele frequencies among individuals within population is
> expected to take negative values, as 2 genes taken from 2 different
> individuals are more similar than two genes taken from the same individual.
> See Weir & Cockerham (1984) Evolution for instance.
>
>
>
>
> Ben Bolker wrote:
>
>   Pardon my asking, but why? For consistency with older (arguably less
> correct) method-of-moments estimates that could give negative
> estimates?
>
> On Fri, Jul 30, 2010 at 1:32 AM, Chris Brien <Chris.Brien at unisa.edu.au>
> wrote:
>
>
> Dear mixed modellers,
>
> I have a data set that gives me an estimate of 0 for one of the variance
> components. I wanted to allow for the estimate of the component to be
> negative. My search of the documentation led me to believe that this is not
> possible. Am I right, or did I miss something?
>
> Cheers,
>
> Chris Brien
> -----
> University of South Australia
> ADELAIDE  5001  South Australia
> WEB page:  <http://people.unisa.edu.au/Chris.Brien>
>
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>
> --
> Jérôme Goudet
> Dept. Ecology & Evolution
> UNIL-Sorge, CH-1015 Lausanne
>
> mail:jerome.goudet at unil.ch
> Tel:+41 (0)21 692 4242
> Fax:+41 (0)21 692 4265