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Re: st: RRR with CI from logit model


From   Constantine Daskalakis <C_Daskalakis@mail.jci.tju.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RRR with CI from logit model
Date   Tue, 02 Nov 2004 12:19:28 -0500

At 06:46 AM 11/2/2004, Michael Ingre wrote:
On 2004-11-02, at 11.35, Ronán Conroy wrote:
Take a step back here. Have you *graphed* your outcome against your predictor variable?
Thanks for your advice. Yes I have graphed it. And there is a squared component that kicks in at about 7 on the scale were probabilities starts to rise dramatically. The graphed probabilities looks fine and are according to theory.

The problem is the standard errors in the predicted RRR using -nlcom-. There seem to be a paradoxical relation here: the more extreme the RRR the LESS significant they are.

The paradox described above can be found in auto.dta also. Consider a logit model where the probability of a car being foreign is modelled as a function of length. Length is negatively associated with foreign (-.0797353). Using -nlcom- a significant (p<.001) ratio of 1.3 between the predicted probabilities are fond for length=1 vs length=10. When length=1 is compared to length=100 the ratio increase to 764 but is no longer significant (p=.606). Code is listed below:

sysuse auto
logit foreign length

// RRR for length=1 vs length=10
nlcom (exp(1 * _b[length] + _cons) / (1+ exp(1 * _b[length] + _cons))) / ///
(exp(10 * _b[length] + _cons) / (1+ exp(10 * _b[length] + _cons))) //

// RRR for length=1 vs length=100
nlcom (exp(1 * _b[length] + _cons) / (1+ exp(1 * _b[length] + _cons))) / ///
(exp(100 * _b[length] + _cons) / (1+ exp(100 * _b[length] + _cons))) //

I might be doing something I shouldn't and I'm happy for any advice on how to calculate RRRs with CI from the logit model above using auto.dta.

Michael
This is not an issue of model fit or any such. The issues raised re linear probability models etc are valid, but they are different from what you are reporting here, I think).

According to my read of the manual, -nlcom- uses the multivariate delta method to perform a Wald-type test on the quantity you're interested (here the RRR).

Look at the estimates and estimated standard errors for the different situations in your example. You'll probably find that the estimated RRR increases but its estimated standard error goes to hell (increases much more). This is a problem with Wald-type tests that has been pointed out before (eg, see Hauck & Donner, JASA 1977, w/ corrrection in 1980). The delta method (especially for anti-log functions of coefficients) seems to exacerbate that.

CD



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________________________________________________________________
Constantine Daskalakis, ScD
Assistant Professor,
Biostatistics Section, Thomas Jefferson University,
211 S. 9th St. #602, Philadelphia, PA 19107
Tel: 215-955-5695
Fax: 215-503-3804
Email: c_daskalakis@mail.jci.tju.edu
Webpage: http://www.jefferson.edu/medicine/pharmacology/bio/

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