Logistic Regression using glm
One of these is modelling the mean of the logit of p, the other is modelling the logit of the mean of p. They aren't the same. -thomas
On Tue, 11 Oct 2005, Daniel Pick wrote:
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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Thomas Lumley Assoc. Professor, Biostatistics tlumley at u.washington.edu University of Washington, Seattle