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

Wed Jun 21 23:53:07 CEST 2023

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
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> 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
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> 
> 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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