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Re: st: Osius-Rojek, Stukel's goodness of fit tests for Logistic Regression

From   Jim Hancock <>
Subject   Re: st: Osius-Rojek, Stukel's goodness of fit tests for Logistic Regression
Date   Mon, 11 Oct 2004 17:51:04 +0930

Dear Brian

I can't answer your specific question on how to implement these tests,
but one interesting consideration of goodness-of-fit (as opposed to
significance) is J.S. Cramer (1999), 'Predictive performance of the
binary logit model in unbalanced samples', The Statistician, 48, Part 1,
pp. 85-94.

He proposes a measure 'lambda' which is a measure of how much better
your model does than if you just used uniform probabilities to predict
the binary outcome.  If you do no better than the naive 'uniform
probability' assumption lambda is zero;  if you improve by 100 per cent
(i.e. predict perfectly) lambda is 1.  He argues that lambda is
analagous to R-squared in linear regression.

I've used this on large unit record databases where the regressions are
highly significant but the lambda is very low, with the model predicting
only 5% better than the naive uniform probability assumption - obviously
a significant qualification to the high statistical significance.

Hope this helps


> Date: Sun, 10 Oct 2004 08:18:51 +0000
> From:
> Subject: st: Osius-Rojek, Stukel's goodness of fit tests for Logistic Regression
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> Dear Colleagues:
>     Does anyone know how to implement an Osius-Rojek goodness of fit test (it is a normal approximation to the Pearson Chi-square statistic) for a logistic regression model using Stata commands?  How about Stukel's test? I'm constructing a logistic regression model on a very large database and the Hosmer Lemeshow statistic indicates that the model does not "fit", however this is in part due to the sample size of the model. Hosmer and Lemeshow in their textbook, Applied Logistic Regression, recommend two other goodness of fit tests to go with their statistic, Osius-Rojek and Stukel.  Any help that you can give me in implementing either of these tests, or any advice on using Stata to assess the goodness of fit in a logistic regression model when the sample size is large would be greatly appreciated.  Thanks!
>    -Brian

Jim Hancock
Deputy Director
South Australian Centre for Economic Studies
PO Box 125
Ph:     +61 8 8303 5515
Fax:    +61 8 8232 5307
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