[R] Logistic Regression using glm

[Sung, Iyue]

You're fitting two different models.

The latter is saying: logit(p)=x+e, where e is a normal error, so that
logit(p) is normal.
"lm" fits a Linear Model, which uses normal error.

The former says that p is Bernoulli; and p~Bernoulli does not imply
logit(p) is normal.
A Generalized Linear Model has different options for specifying the
random component.

Agresti's "Categorical Data Analysis" lays out the details very well.

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Daniel Pick
> Sent: Tuesday, October 11, 2005 12:22 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Logistic Regression using glm
> 
> Hello everyone,
>    I am currently teaching an intermediate stats.
> course at UCSD Extension using R.  We are using Venables and 
> Ripley as the primary text for the course, with Freund & 
> Wilson's Statistical Methods as a secondary reference.
>    I recently gave a homework assignment on logistic 
> regression, and I had a question about glm.  Let n be the 
> number of trials, p be the estimated sample proportion, and w 
> be the standard binomial weights n*p*(1-p).  If you perform 
> output <- glm(p ~ x, family = binomial, weights = n) you get 
> a different result than if you perform the logit 
> transformation manually on p and perform output <- 
> lm(logit(p) ~ x, weights = w), where logit(p) is either 
> obtained from R with
> qlogis(p) or from a manual computation of ln(p/1-p).
> 
> The difference seems to me to be too large to be roundoff 
> error.  The only thing I can guess is that the application of 
> the weights in glm is different than in a manual computation. 
>  Can anyone explain the difference in results?  
> 
> 
> Daniel Pick
> Principal
> Daniel Pick Scientific Software Consulting San Diego, CA
> E-Mail: mth_man at yahoo.com
> 
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