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Re: st: Query..


From   Richard Goldstein <richgold@ix.netcom.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Query..
Date   Tue, 16 Apr 2013 21:00:58 -0400

Tony, et al.

the quote is "To make the preliminary test on variances is rather like
putting to sea in a rowing boat to findout whether conditions are
sufficiently calm for an ocean liner to leave port!"

this is on p. 333 of Box, GEP (1953), "Non-normality and tests on
Variances," _Biometrika_, 40 (3/4): 318-335

Rich

On 4/16/13 7:01 PM, Lachenbruch, Peter wrote:
> The context i was referring to was an old article by George Box in Biometrika 
aboutg 1953 in which he commented that testing for heteroskedasticy was
like setting
to see in a rowboat to see if it was safe for the Queen Mary to sail.
Sorry i don't
have the quote, and my books are all bundled up due to a flood in my
basement
> 
> Peter A. Lachenbruch,
> Professor (retired)
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of John Antonakis [John.Antonakis@unil.ch]
> Sent: Tuesday, April 16, 2013 1:47 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Query..
> 
> Hello Peter:
> 
> Can you please elaborate? The chi-square test of fit--or the likelihood
> ratio test comparing the saturated to the target model--is pretty
> robust, though as I indicated, it does not behave as expected at small
> samples, when data are not multivariate normal, when the model is
> complex (and the n to parameters estimated ration is low). However, as I
> mentioned there are remedies to the problem. More specifically see:
> 
> Bollen, K. A., & Stine, R. A. (1992). Bootstrapping goodness-of-fit
> measures in structural equation models. Sociological Methods & Research,
> 21(2), 205-229.
> 
> Herzog, W., & Boomsma, W. (2009). Small-sample robust estimators of
> noncentrality-based and incremental model fit. Structural Equation
> Modeling, 16(1), 1–27.
> 
> Swain, A. J. (1975). Analysis of parametric structures for variance
> matrices (doctoral thesis). University of Adelaide, Adelaide.
> 
> Yuan, K. H., & Bentler, P. M. (2000). Three likelihood-based methods for
> mean and covariance structure analysis with nonnormal missing data. In
> M. E. Sobel & M. P. Becker (Eds.), Sociological Methodology (pp.
> 165-200). Washington, D.C: ASA.
> 
> In addition to elaborating, better yet, if you have a moment give us
> some syntax for a dataset that you can create where there are
> simultaneous equations with observed variables, an omitted cause, and
> instruments. Let's see how the Hansen-J test (estimated with reg3, with
> 2sls and 3sls) and the normal theory chi-square statistic (estimated
> with sem) behave (with and with robust corrections).
> 
> Best,
> J.
> 
> __________________________________________
> 
> John Antonakis
> Professor of Organizational Behavior
> Director, Ph.D. Program in Management
> 
> Faculty of Business and Economics
> University of Lausanne
> Internef #618
> CH-1015 Lausanne-Dorigny
> Switzerland
> Tel ++41 (0)21 692-3438
> Fax ++41 (0)21 692-3305
> http://www.hec.unil.ch/people/jantonakis
> 
> Associate Editor
> The Leadership Quarterly
> __________________________________________
> 
> On 16.04.2013 22:04, Lachenbruch, Peter wrote:
>> I would be rather cautious about relying on tests of variances.  These are notoriously non-robust.  Unless new theory has shown this not to be the case, i'd not regard this as a major issue.
>>
>> Peter A. Lachenbruch,
>> Professor (retired)
>> ________________________________________
>> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of John Antonakis [John.Antonakis@unil.ch]
>> Sent: Tuesday, April 16, 2013 10:51 AM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: Query..
>>
>> In general I find Acock's books helpful and I have bought two of them.
>> The latest one he has on SEM was gives a very nice overview of the SEM
>> module in Stata. However, it is disappointing on some of the statistical
>> theory, in particular with respect to fact that he gave too much
>> coverage to "approximate" indexes of overidentification, which are not
>> tests, and did not explain enough what the chi-square statistic of
>> overidentification is.
>>
>> The Stata people are usually very good about strictly following
>> statistical theory, as do all econometricians, and do not promote too
>> much these approximate indexes.  So, I was a bit annoyed to see how much
>> airtime was given to rule-of-thumb indexes that have no known
>> distributions and are not tests. The only serious test of
>> overidentification, analogous to the Hansen-Sargen statistic is the
>> chi-square test of fit. So, my suggestion to Alan is that he spends some
>> time to cover that in the updated addition and not to suggest that
>> models that fail the chi-square test are "approximately good."
>>
>> For those who do not know what this statistic does, it basically
>> compares the observed variance-covariance (S) matrix to the fitted
>> variance covariance matrix (sigma) to see if the difference (residuals)
>> are simultaneously different from zero. The fitting function that is
>> minimized is:
>>
>> Fml =  ln|Sigma| - ln|S| + trace[S.Sigma^-1] - p
>>
>> As Sigma approaches S, the log of the determinant of Sigma less the log
>> of the determinant of S approach zero; as concerns the two last terms,
>> as Sigma approaches S, the inverse of Sigma premultiplied by S makes an
>> identity matrix, whose trace will equal the number of observed variables
>> p (thus, those two terms also approach zero). The chi-square statistic
>> is simply Fml*N, at the relevant DF (which is elements in the
>> variance-covariance matrix less parameters estimated).
>>
>> This chi-square test will not reject a correctly specified model;
>> however, it does not behave as expected at small samples, when data are
>> not multivariate normal, when the model is complex (and the n to
>> parameters estimated ration is low), which is why several corrections
>> have been shown to better approximate the true chi-square distribution
>> (e.g., Swain correction, Yuan-Bentler correction, Bollen-Stine bootstrap).
>>
>> In all, I am thankful to Alan for his nice "how-to" guides which are
>> very helpful to students who do not know Stata need a "gentle
>> introduction"--so I recommend them to my students, that is for sure.
>> But, I would appreciate a bit more beef from him for the SEM book in
>> updated versions.
>>
>> Best,
>> J.
>>
>> __________________________________________
>>
>> John Antonakis
>> Professor of Organizational Behavior
>> Director, Ph.D. Program in Management
>>
>> Faculty of Business and Economics
>> University of Lausanne
>> Internef #618
>> CH-1015 Lausanne-Dorigny
>> Switzerland
>> Tel ++41 (0)21 692-3438
>> Fax ++41 (0)21 692-3305
>> http://www.hec.unil.ch/people/jantonakis
>>
>> Associate Editor
>> The Leadership Quarterly
>> __________________________________________
>>
>> On 16.04.2013 17:45, Lachenbruch, Peter wrote:
>>   > David -
>>   > It would be good for you to specify what you find problematic with
>> Acock's book.  I've used it and not had any problems - but maybe i'm
>> just ancient and not seeing issues
>>   >
>>   > Peter A. Lachenbruch,
>>   > Professor (retired)
>>   > ________________________________________
>>   > From: owner-statalist@hsphsun2.harvard.edu
>> [owner-statalist@hsphsun2.harvard.edu] on behalf of Hutagalung, Robert
>> [Robert.Hutagalung@med.uni-jena.de]
>>   > Sent: Monday, April 15, 2013 2:06 AM
>>   > To: statalist@hsphsun2.harvard.edu
>>   > Subject: AW: st: Query..
>>   >
>>   > Hi David,
>>   > Thanks, though I find the book very useful.
>>   > Best, Rob
>>   >
>>   > -----Ursprüngliche Nachricht-----
>>   > Von: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von David Hoaglin
>>   > Gesendet: Samstag, 13. April 2013 16:11
>>   > An: statalist@hsphsun2.harvard.edu
>>   > Betreff: Re: st: Query..
>>   >
>>   > Hi, Rob.
>>   >
>>   > I am not able to suggest a book on pharmacokinetics/pharmacodynamics,
>>   > but I do have a comment on A Gentle Introduction to Stata.  As a
>> statistician, I found it helpful in learning to use Stata, but a number
>> of its explanations of statistics are very worrisome.
>>   >
>>   > David Hoaglin
>>   >
>>   > On Fri, Apr 12, 2013 at 9:01 AM, Hutagalung, Robert
>> <Robert.Hutagalung@med.uni-jena.de> wrote:
>>   >> Hi everyone, I am a new fellow here..
>>   >> I am wondering if somebody could  a book (or books) on Stata dealing
>> with pharmacokinetics/pharmacodinamics - both analyses and graphs.
>>   >> I already have: A Visual Guide to Stata Graphics, 2' Edition, A
>> Gentle Introduction to Stata, Third Edition, An Introduction to Stata
>> for Health Researchers, Third Edition.
>>   >> Thanks in advance, Rob.
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