[R-sig-ME] Standard errors of variances; negative variance

Thu Jun 22 03:32:34 CEST 2023

This negative variance issue crops up in factor analysis oftentimes with
Heywood cases etc. One approach that has often been invoked in this
literature is to set them to zero, though it has been some time since I
have delved deep into this literature.

On Wed, Jun 21, 2023 at 9:16 PM John H Maindonald <jhmaindonald using gmail.com>
wrote:

> Another way to look at the issue is that variance components are just
> that — components that cannot necessarily be interpreted as variances.
> They cannot even necessarily be interpreted in a particularly meaningful
> way as variances, even if the values come out as positive.
> John Maindonald
> Statistics Research Associates, Wellington NZ.
>
> Dear  All,
> As with the square root of -1, negative variances are a convenient
> computational fiction.  The square root of -1 is an invitation to move
> to a 2-dimensional word, where they make perfect sense.
>
> A negative variance estimate, in those systems that allow it, is a useful
> warning that one needs to think and move beyond the one-dimensional
> representation in which the variances have been set.
> John Maindonald
> Statistics Research Associates, Wellington NZ.
>
> > On 21/06/2023, at 01:21, Sorkin, John <jsorkin using som.umaryland.edu> wrote:
> >
> >
> > Thierry,
> > I have the same question that you posed, how can a variance, a measure
> that is squared be negative? Will, please enlighten us!
> > John
> > John David Sorkin M.D., Ph.D.
> > Professor of Medicine
> > Chief, Biostatistics and Informatics
> > University of Maryland School of Medicine Division of Gerontology and
> Geriatric Medicinet
> > Baltimore VA Medical Center
> > 10 North Greene Street<x-apple-data-detectors://12>
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> > Baltimore, MD 21201-1524<x-apple-data-detectors://13/0>
> > (Phone) 410-605-711<tel:410-605-7119>9
> > (Fax) 410-605-7913<tel:410-605-7913> (Please call phone number above
> prior to faxing)
> >
> > On Jun 20, 2023, at 3:45 AM, Thierry Onkelinx via R-sig-mixed-models <
> r-sig-mixed-models using r-project.org> wrote:
> >
> > Dear all,
> >
> > A negative variance seems odd to me. Isn't a variance positive by
> > definition? How would you interpret a random intercept with a negative
> > variance?
> >
> > Best regards,
> >
> > ir. Thierry Onkelinx
> > Statisticus / Statistician
> >
> > Vlaamse Overheid / Government of Flanders
> > INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
> AND
> > FOREST
> > Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> > thierry.onkelinx using inbo.be
> > Havenlaan 88 bus 73, 1000 Brussel
> >
> https://nam11.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.inbo.be%2F&data=05%7C01%7Cjsorkin%40som.umaryland.edu%7C2c0d1047636b43c2bfcc08db71625f82%7C717009a620de461a88940312a395cac9%7C0%7C0%7C638228439560019013%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=sbP2Xemwg0iHjvxcc6zR8vtPbZf5ZoFCv1BIFIeDdBE%3D&reserved=0
> >
> >
> ///////////////////////////////////////////////////////////////////////////////////////////
> > To call in the statistician after the experiment is done may be no more
> > than asking him to perform a post-mortem examination: he may be able to
> say
> > what the experiment died of. ~ Sir Ronald Aylmer Fisher
> > The plural of anecdote is not data. ~ Roger Brinner
> > The combination of some data and an aching desire for an answer does not
> > ensure that a reasonable answer can be extracted from a given body of
> data.
> > ~ John Tukey
> >
> ///////////////////////////////////////////////////////////////////////////////////////////
> >
> > <
> https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.inbo.be%2F&data=05%7C01%7Cjsorkin%40som.umaryland.edu%7C2c0d1047636b43c2bfcc08db71625f82%7C717009a620de461a88940312a395cac9%7C0%7C0%7C638228439560019013%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=I5HJ05o0Bd4ly0GL0Smc1iYm3cuZMc2IGCcxy8OWn%2B8%3D&reserved=0
> >
> >
> >
> > Op di 20 jun 2023 om 01:36 schreef Ben Bolker <bbolker using gmail.com>:
> >
> > Hi, Will,
> >
> > Googling
> >
> > site:
> https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fpipermail%2Fr-sig-mixed-models%2F&data=05%7C01%7Cjsorkin%40som.umaryland.edu%7C2c0d1047636b43c2bfcc08db71625f82%7C717009a620de461a88940312a395cac9%7C0%7C0%7C638228439560019013%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=vw%2FnMxnvA7L9A0qYuJfHa9suA2YBTnZ%2BqxPltyR3G%2FU%3D&reserved=0
> "negative
> > variance"
> >
> > claims to get you 67 results (although only 11 that Google considers
> > worth displaying by default),
> >
> > You can filter by date - there are only two hits since 2020:
> >
> >
> >
> https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.google.com%2Fsearch%3Fq%3Dsite%253Ahttps%253A%252F%252Fstat.ethz.ch%252Fpipermail%252Fr-sig-mixed-models%252F%2B%2522negative%2Bvariance%2522%26client%3Dfirefox-b-d%26tbs%3Dcdr%253A1%252Ccd_min%253A01-01-2020%252Ccd_max%253A%26tbm%3D&data=05%7C01%7Cjsorkin%40som.umaryland.edu%7C2c0d1047636b43c2bfcc08db71625f82%7C717009a620de461a88940312a395cac9%7C0%7C0%7C638228439560019013%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=xbWrjRwClEMYFKVkncDFgZga6SPNcmsPvbNs4kpUQjY%3D&reserved=0
> >
> >
> > and these both look like false positives (they include "negative" and
> > "variance" but not "negative variance" ...)
> >
> > The short answer is that I am not aware of any mixed effect package
> > in R that will allow you to return negative values. You can see my
> > answer here:
> >
> https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fpipermail%2Fr-sig-mixed-models%2F2018q1%2F026437.html&data=05%7C01%7Cjsorkin%40som.umaryland.edu%7C2c0d1047636b43c2bfcc08db71625f82%7C717009a620de461a88940312a395cac9%7C0%7C0%7C638228439560019013%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=2E5S51uIXiPEsuH11f693MEOLYFb2dh5e39t2GSLor8%3D&reserved=0
> ...
> >
> >
> > As for uncertainties in variances - the merDeriv package (dating back
> > to 2017) will give you the standard errors of variances and covariances
> > (although again, note that there's a theoretical issue here - the
> > standard errors are often extremely poor summaries of the uncertainty or
> > RE variances, the original authors of lme4 would certainly prefer that
> > you use profile confidence intervals to summarize the uncertainty ...)
> >
> > That's what I know -- perhaps someone else knows about a package that
> > allows for negative variances ... ??
> >
> > On 2023-06-19 6:13 p.m., Will Hopkins wrote:
> > I've just joined this list to get answers to a few questions. I would
> > have
> > searched the archive before posting, but there seems to be no way of
> > searching except via quarterly summaries. I searched the last four
> > quarters
> > without success.
> >
> > I'm a SAS user, but a few years ago I tried the mixed model in R, with
> > the
> > help of an R user (Alice Sweeting). At that time, the lme package did not
> > provide standard errors for the variances, nor did it allow negative
> > variance. Have these limitations been addressed?  As I recall, Alice
> > found
> > some code that provided standard errors, but it gave values different
> > from
> > those of the mixed model in SAS (Proc Mixed). I therefore opted to stay
> > with
> > SAS, because allowing for negative variance for random effects other than
> > residuals and estimating uncertainties in variances are both fundamental
> > to
> > mixed modeling, in my view. I also became fluent with SAS coding over the
> > years and did not want to make the effort with R coding. Interestingly,
> > SAS
> > introduced a free cloud version called SAS Studio, evidently modeled on R
> > Studio, to try to win back customers!
> >
> > Will
> >
> > _______________________________________________
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