# [R] Pseudo R^2 for logit - really naive question

Paul M. Jacobson pmj at jciconsult.com
Wed Aug 7 14:03:56 CEST 2002

```I could find the function in the function search option on CRAN.  However,
how to find the actual library remains a mystery to me.  I could not see it
under the list of available bundles and packages on the CRAN site
http://lib.stat.cmu.edu/R/CRAN/sources.html
I am very much a newbie to the R world and need some more direct help.

-----Original Message-----
From: owner-r-help at stat.math.ethz.ch
[mailto:owner-r-help at stat.math.ethz.ch]On Behalf Of Frank E Harrell Jr
Sent: August 4, 2002 11:36 AM
To: pmj at jciconsult.com
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] Pseudo R^2 for logit - really naive question

The Nagelkerke R^2 is commonly used.   The lrm function in the Design
library computes this for logistic regression.  The numerator is 1 -
exp(-LR/n) where LR is the likelihood ratio chi-square stat and n is the
total sample size.  Divide it by the maximum attainable value of this if the
model is perfect (which is a simple function of the -2 log likelihood with
an intercept-only model) to get Nagelkerke's R^2.  The numerator is exactly
the ordinary R^2 in OLS, as LR = -n log(1-R^2) there.  For a more
interpretable index and one that measures purely discrimination ability, the
ROC area or "C index" which is essentially a Mann-Whitney statistic based on
concordance probability is recommended.  The lrm function also outputs this
or you can get it from the somers2 or rcorr.cens functions in the Hmisc
library.

Frank Harrell

On Sun, 4 Aug 2002 09:08:46 -0400
"Paul M. Jacobson" <pmj at jciconsult.com> wrote:

> I am using GLM to calculate logit models based on cross-sectional data.  I
> am now down to the hard work of making the results intelligible to very
> average readers.  Is there any way to calculate a psuedo analoque to the
R^2
> in standard linear regression for use as a purely descriptive statistic of
> goodness of fit? Most of the readers of my report will be vaguely familiar
> and more comfortable with R^2 than with any other regression diagnostics.
>
> Paul M. Jacobson
> Jacobson Consulting Inc.
> 80 Front Street East, Suite 720
> Toronto, ON, M5E 1T4
> Voice:  +1(416)868-1141
> Farm: +1(519)463-6061/6224
> Fax: +1(416)868-1131
> E-mail: pmj at jciconsult.com
> Web:  http://www.jciconsult.com/
>
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--
Frank E Harrell Jr              Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine  http://hesweb1.med.virginia.edu/biostat
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