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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 |

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. > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ > > Universitätsklinikum Jena - Bachstrasse 18 - D-07743 Jena > Die gesetzlichen Pflichtangaben finden Sie unter http://www.uniklinikum-jena.de/Pflichtangaben.html > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Query..***From:*"Hutagalung, Robert" <Robert.Hutagalung@med.uni-jena.de>

**Re: st: Query..***From:*David Hoaglin <dchoaglin@gmail.com>

**AW: st: Query..***From:*"Hutagalung, Robert" <Robert.Hutagalung@med.uni-jena.de>

**RE: st: Query..***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: Query..***From:*John Antonakis <John.Antonakis@unil.ch>

**RE: st: Query..***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: Query..***From:*John Antonakis <John.Antonakis@unil.ch>

**RE: st: Query..***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: Query..***From:*John Antonakis <John.Antonakis@unil.ch>

**Re: st: Query..***From:*Nick Cox <njcoxstata@gmail.com>

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