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Re: FW: st: Query..


From   "Roger B. Newson" <r.newson@imperial.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: FW: st: Query..
Date   Wed, 17 Apr 2013 11:18:00 +0100

A more rigorous demonstration of this point, and other points about the 2-sample t-test, using numerical integration, is given in Moser, Stevens and Watts (1989) and in Moser and Stevens (1992).

Best wishes

Roger

References

Moser, B.K., Stevens, G.R., and Watts, C.L. 1989. The two-sample t-test
versus Satterthwaite’s approximate F-test. Communications in Statistics - Theory and Methods 18, 3963-3975.

Moser, B.K. and Stevens, G.R. 1992. Homogeneity of variance in the two-sample means test. The American Statistician 46, 19-21.

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 17/04/2013 04:26, Lachenbruch, Peter wrote:
Rich Goldstein sent this to me

Peter A. Lachenbruch,
Professor (retired)
________________________________________
From: Richard Goldstein [richgold@ix.netcom.com]
Sent: Tuesday, April 16, 2013 6:00 PM
To: statalist@hsphsun2.harvard.edu
Cc: Lachenbruch, Peter
Subject: Re: st: Query..

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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