From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Sat 16 Jul 2005 - 01:22:17 EST

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Jul 16 01:26:26 2005

Date: Sat 16 Jul 2005 - 01:22:17 EST

On Fri, 15 Jul 2005, Robin Hankin wrote:

> I am trying to make glm() work to analyze a toy logit system.

*>
**> I have a dataframe with x and y independent variables. I have
**>
**> L=1+x-y (ie coefficients 1,1,-1)
**>
**> then if I have a logit relation with L=log(p/(1-p)),
**> p=1/(1+exp(L)).
*

Not quite, see below.

> If I interpret "p" as the probability of success in a Bernouilli

*> trial, and I can observe the result (0 for "no", 1 for "yes")
**> how do I retrieve the coefficients c(1,1,-1)
**> from the data?
**>
**> n <- 300
**> des <- data.frame(x=(1:n)/n,y=sample(n)/n) # experimental design
**> des <- cbind(des,L=1+des$x-des$y) # L=1+x-y
**> des <- cbind(des,p=1/(1+exp(des$L))) # p=1/(1+e^L)
*

A logit would be p = e^L/(1+e^L), so your signs for L are reversed.

> des <- cbind(des,obs=rbinom(n,1,des$p)) # observation: prob of

*> success = p.
**>
**>
**> My attempt is:
**>
**> glm(obs~x+y,data=des,family=binomial(link="logit"))
**>
**> But it does not retrieve the correct coefficients of c(1,1,-1) ;
**> I would expect a reasonably close answer with so much data.
*

You actually have so little data.

> What is the correct glm() call to perform my logit analysis?

The call is correct, the expectation is not. A single bernoulli observation provides far less information than you seem to suppose.

I got

Coefficients:

Estimate Std. Error z value Pr(>|z|) (Intercept) -1.4747 0.3670 -4.019 5.85e-05 *** x -0.5549 0.4672 -1.188 0.23494 y 1.2963 0.4731 2.740 0.00614 **

and note how large the standard errors are. With 10000 examples you will get closer. Having fixed your sign change, I got

Coefficients:

Estimate Std. Error z value Pr(>|z|) (Intercept) 0.98711 0.06024 16.39 <2e-16 *** x 1.00896 0.08052 12.53 <2e-16 *** y -0.87798 0.08031 -10.93 <2e-16 *** -- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sat Jul 16 01:26:26 2005

*
This archive was generated by hypermail 2.1.8
: Fri 03 Mar 2006 - 03:33:45 EST
*