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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

Subject |
RE: ST: st: Logistic regression & standardized coefficients; Multinomial GOF test |

Date |
Thu, 8 Dec 2011 12:03:20 -0500 |

Hi Ron, It may make sense to standardize only with respect to X (predictors), which is easy to do. But maybe have a look at some of the more complicated formulas in: Menard, S. (2011). Standards for Standardized Logistic Regression Coefficients. Social Forces, 89(4), 1409-1428. Menard, S. (2004). Six Approaches to Calculating Standardized Logistic Regression Coefficients. The American Statistician, 58, 218-223. I think it might be fairly straightforward to extend them to the nominal case. That said, you would have to think hard about whether it makes sense to standardize the predictors. This may only make sense with continuous predictors, and in my view it does not render effects comparable, because standard deviations differ across predictors and also across groups on the same predictor. I think the cautions in the following papers would apply: King, G. (1986). How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science. American Journal of Political Science, 30(3), 666-687.http://gking.harvard.edu/files/mist.pdf>http://gking.harvard.edu/files/mist.pdf Richards, J.M., Jr. (1982). Standardized versus Unstandardized Regression Weights. Applied Psychological Measurement, 6(2), 201-212. Greenland, S., Schlessman, J.J., & Criqui, M.H. (1986). The fallacy of employing standardized regression coefficients and correlations as measures of effect. American Journal of Epidemiology, 123, 203–208. Greenland, S., Maclure, M., Schlessman, J.J., Poole, C., & Morgenstern, H. (1991). Standardized Regression Coefficients: A Further Critique and Review of Some Alternatives. Epidemiology, 2(5). 387-392. Criqui, M.H. (1991). On the Use of Standardized Regression Coefficients. Epidemiology, 2(5), 393. Hargens, L.L. (1976). A Note On Standardized Coefficients as Structural Parameters. Sociological Methods & Research, 5(2), 247-256 Kim, J.O., & Feree, G. D. (1981). Standardization in causal analysis. Sociological Methods and. Research, 10(2), 187–210. Best, Cam > From: McDowell-R3@email.ulster.ac.uk > To: statalist@hsphsun2.harvard.edu > Subject: ST: st: Logistic regression & standardized coefficients; Multinomial GOF test > Date: Thu, 8 Dec 2011 16:10:08 +0000 > > > I see from the literature (eg Long and Freese' STATA regression book and as used by fitstat), one approach to logistic regression models is the latent variable model, where y*, the extent/propensity to which one > favours one option as opposed to the other, can be written as a linear combination of predictors plus an error term, the latter which has a standard logistic distribution with variance pi-squared/3. By definition > this is the result for a multinomial (logit) model with 2 classes. Is anyone aware of any references which allow this to be generalised to 3 or more classes, for example, so that y* can be calculated > at each of the different levels (relative to the baseline), as a linear combination plus an error term whose distribution is known and hence can be computed? > > Many thanks (again) > > Ron > > > ------------------------------ > > Date: Wed, 7 Dec 2011 14:31:45 +0000 > From: Ronald McDowell <McDowell-R3@email.ulster.ac.uk> > Subject: st: Re: St: Logistic regression & standardized coefficients; Multinomial GOF test > > Richard > > Thanks for the excellent references (below). A follow-up question is whether there is such a thing as standardized coefficients in multinomial logistic regression models, > and if so if there are any parallel references. > > Many thanks > > Ron McDowell > - ----------------------------------------- > Ron McDowell > Institute of Nursing Research > University of Ulster, Coleraine > McDowell-R3@email.ulster.ac.uk > > > Date: Tue, 06 Dec 2011 12:14:22 -0500 > From: Richard Williams <richardwilliams.ndu@gmail.com> > Subject: Re: st: St: Logistic regression & standardized coefficients; Multinomial GOF test > > At 11:55 AM 12/6/2011, Ronald McDowell wrote: > >Hi all > > > >1. I've been looking at some materials online about standardized > >coefficients in logistic regression eg. > > > > > >http://www.nd.edu/~rwilliam/stats3/L06.pdf > > > >Full standardization includes dividing the estimated coefficients by > >the standard deviation of Y*. Can someone clarify for me what > >exactly Y* is ? I'm aware it is a function of the fitted values. I > >have used listcoef and fitstat to obtain sd(Y*) so far, but > > would like to be able to manually compute it. > > See Long & Freese's book for a detailed explanation: > > http://www.stata.com/bookstore/regmodcdvs.html > > For a mini-explanation, including how to compute manually, see > > http://www.nd.edu/~rwilliam/xsoc73994/L03.pdf > > For more advanced discussions, see the first 19 slides of > > http://www.nd.edu/~rwilliam/stats/Oglm.pdf > > Also take a look at the -khb- command on SSC and the papers > associated with it. The relevant papers may still be forthcoming so > you may need to write the authors if you want them. > > Finally, I don't have the full citation handy, but Scott Menard > offered an alternative approach to Y-standardization in a 2010 issue > of Social Forces. > > - - ------------------------------------------- > Richard Williams, Notre Dame Dept of Sociology > OFFICE: (574)631-6668, (574)631-6463 > HOME: (574)289-5227 > EMAIL: Richard.A.Williams.5@ND.Edu > WWW: http://www.nd.edu/~rwilliam > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/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/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/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/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**ST: st: Logistic regression & standardized coefficients; Multinomial GOF test***From:*Ronald McDowell <McDowell-R3@email.ulster.ac.uk>

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