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| 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. * * 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/