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Re: st: Query..


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Query..
Date   Wed, 17 Apr 2013 12:41:30 +0200

Right....that is precisely the point I have made about having a rescaled chi-square test of the sort cited here:

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.

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 17.04.2013 12:37, Nick Cox wrote:
You are simulating well-behaved data -- I see -rnormal()- everywhere
-- but the doubts raised are about how well tests perform in
non-standard situations.
Nick
njcoxstata@gmail.com


On 17 April 2013 11:28, John Antonakis <John.Antonakis@unil.ch> wrote:
OK....fine with this, but it has no bearing whatsoever on what I said below,
which was on overidentification and how it is tested in SEM. The chi-square
statistic of SEM will be very similar to the overidentification statistic
from a 2sls or 3sls model, and that is the point I was trying to get across.
So, if economists (and others) trust the Hansen-Sargan overidentification
statistic, then they should trust and sem chi-square overidentification
statistic (and not indexes that are not tests).

Run this code to see that we can about the same chi-square value whether
using 2sls or sem, even though they go about it in very different way (i.e.,
in 2sls, chi = r-square*N from a regression of the residuals of the y
equation on the excluded in instruments, whereas the chi-square test from
SEM uses the discrepancy function I showed below from sigmal and S):

clear
set seed 123
set obs 1000

gen  x1 = rnormal()
gen  x2 = rnormal()
gen q = rnormal()
gen m = x1 + x2 - q + rnormal()
gen y = m + q + rnormal()

qui: ivregress 2sls y (m = x1 x2)
qui: estat overid
scalar chi_sargan = r(sargan)
scalar p_sargan =  r(p_sargan)

qui: sem (y<-m) (m<-x1 x2), cov(e.y*e.m)
qui: estat gof
scalar chi_sem = r(chi2_ms)
scalar p_sem = r(p_ms)

dis "Chi Sargan = "chi_sargan ", p-value = "p_sargan
dis "Chi SEM = "chi_sem ", p-value = "p_sem

Now, having latent variable in there does not change the basis of how this
chi-square statistic is calculated in SEM. Also, if we have one of the
conditions that makes the chi-square misbehave (that I identified below),
then we can rescale the SEM chi-square using one of the corrective
procedures so that it approximates the expected chi-square distribution.


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 17.04.2013 01:01, 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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