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Re: st: Query..
From
Richard Goldstein <[email protected]>
To
[email protected]
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: [email protected] [[email protected]] on behalf of John Antonakis [[email protected]]
> Sent: Tuesday, April 16, 2013 1:47 PM
> To: [email protected]
> 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: [email protected] [[email protected]] on behalf of John Antonakis [[email protected]]
>> Sent: Tuesday, April 16, 2013 10:51 AM
>> To: [email protected]
>> 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: [email protected]
>> [[email protected]] on behalf of Hutagalung, Robert
>> [[email protected]]
>> > Sent: Monday, April 15, 2013 2:06 AM
>> > To: [email protected]
>> > Subject: AW: st: Query..
>> >
>> > Hi David,
>> > Thanks, though I find the book very useful.
>> > Best, Rob
>> >
>> > -----Ursprüngliche Nachricht-----
>> > Von: [email protected]
>> [mailto:[email protected]] Im Auftrag von David Hoaglin
>> > Gesendet: Samstag, 13. April 2013 16:11
>> > An: [email protected]
>> > 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
>> <[email protected]> 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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