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RE: st: Small standard errors of the parameters in logit models


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Small standard errors of the parameters in logit models
Date   Thu, 15 Dec 2011 08:03:43 -0500

Large N is typically required to obtain precision in the logistic case:

Nemes, S., Jonasson, J.M., Genell, A., & Steineck, G. (2009). Bias in odds ratios by logistic regression modelling and sample size. BMC Medical Research Methodology, 9(56).http://www.biomedcentral.com/content/pdf/1471-2288-9-56.pdf

Bergtold, J.S., Yeager, E.A., & Featherstone, A. (July, 2011). Sample Size and Robustness of Inferences from Logistic Regression in the Presence of Nonlinearity and Multicollinearity. Selected Paper prepared for presentation at the Agricultural & Applied EconomicsAssociation’s 2011 AAEA & NAREA Joint Annual Meeting, Pittsburgh, Pennsylvania, July 24-26, 2011.http://ageconsearch.umn.edu/bitstream/103771/2/Bergtold%20et%20al.%20Logit%20Bias%20Paper.pdf

Nick is correct. You should be looking examining the effect sizes and making an informed judgment of their meaningfulness, based on your subject matter knowledge and research context. Ideally, you would have identified a meaningful effect size a priori and conducted a power analysis. Anyway, perhaps the following will be of use to you:

Breaugh, J.A. (2003). Effect Size Estimation: Factors to Consider and Mistakes to Avoid. Journal of Management, 29(1), 79–97.http://www.owlnet.rice.edu/~antonvillado/courses/09a_psyc630001/Breaugh%20(2003)%20JOM.pdf

Hsieh, F.Y., Bloch, D.A., & Larsen, M.D. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine, 17, 1623-1634.http://personal.health.usf.edu/ywu/logistic.pdf

DeMaris, A. (2002). Explained Variance in Logistic Regression: A Monte Carlo Study of Proposed Measures. Sociological Methods & Research, 31(1), 27-74.http://gabarrot.psychologie-sociale.org/documents/DM2002.pdf

Menard, S. (2000). Coefficients of Determination for Multiple Logistic Regression Analysis. The American Statistician, 54(1), 17-24. 

Liao, J.G., & McGee, D. (2003). Adjusted Coefficients of Determination for Logistic Regression. The American Statistician, 57(3), 161-165. 

Mittlböck, M., & Schemper, M. (1996). Explained variation for logistic regression. Statistics in Medicine, 15(19), 1987-1997.

Mittlböck, M. (1998). Computing measures of explained variation for logistic regression models. Computer Methods and Programs in Biomedicine, 58(1), 17-24.

Allen, J., & Le, H. (2008). An Additional Measure of Overall Effect Size for Logistic Regression Models. Journal of Educational and Behavioral Statistics, 33(4), 416-441.

Cam   

> Date: Thu, 15 Dec 2011 11:15:03 +0000
> Subject: Re: st: Small standard errors of the parameters in logit models
> From: njcoxstata@gmail.com
> To: statalist@hsphsun2.harvard.edu
> 
> There is no evidence here that you need any extra adjustment for
> sample size beyond what is provided automatically  and no indication
> of what it should be even if your view is correct.
> 
> Statistical significance testing historically had one leading role, to
> stop researchers making fools of themselves by over-interpreting
> apparent effects from very small samples. And that is still of some
> importance. However, with very large sample sizes it is no surprise
> that almost anything will be significant, meaning usually definitely
> not zero, and the question becomes one of interpreting the magnitude
> of effects. As you report that the effects are small, that is also
> consistent with what is typical for such datasets.
> 
> Nick
> 
> 2011/12/15 Kai Huang <demonsecret@hotmail.com.hk>:
> > Dear all,
> >
> > I have run a logit model on the employment probability in the labour force using pooled UK LFS data over various years. The estimated parameters are small in magnitude but highly statistically significant. I doubt that it is due to the large sample size rather than proper specification of the model. Does anyone know whether there are any STATA packages that estimate a limited dependent variable model with adjustment of standard errors to large sample size?
> >
> 
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