Thanks for that Daniel, Problem solved. I was mis-specifying the equation, omitting that I had to account for the logit transformation used in family binomial. i.e. had to write y~exp(b+ax+cx^2)/(1+exp(b+ax+cx^2)) to make use of the coeffs
The last part of what I was doing worked, running an lm on the predicted values of a glm, just to get coefficients that could be directly written in an equation of the form y~b+ax+cx^2. But was a silly way of going about it. thank you Samuel --- En date de : Ven 10.10.08, Daniel Malter <[EMAIL PROTECTED]> a écrit : > De: Daniel Malter <[EMAIL PROTECTED]> > Objet: AW: [R] Coefficients in a polynomial glm with family poisson/binomial > À: [EMAIL PROTECTED], r-help@r-project.org > Date: Vendredi 10 Octobre 2008, 19h58 > I don't know what you mean by XCoef x X. But your > problem is (as it works if > you specify "normal" in a glm) that the > functional relationship between your > predictors, i.e. Intercept+X+X^2, and Y is not linear for a > binomial or a > poisson distribution. > > Generalized linear model implies that the model is linear > in the predictors. > It does not mean, however, that the functional relationship > between the > linear predictor and Y is linear. > > E.g. Y=exp(Intercept+X+X^2) is linear in the predictor, but > it is a > nonlinear function because "e" is raised to the > linear predictor. Consult > any book on generalized linear models for more help. > > The estimated coefficients are typically not worthless as > allow you to say > how much your Y will change with a change of delta*x at the > mean of X, for > example, you just have to respect the functional form of > the relationship > between X and Y. Thus, the coefficients you get are > accurate. Just what you > do with them is not. > > For the last part of your question, I am not sure what you > are trying to do > there, but it does not sound right to me in the first > place. > > Cheers, > Daniel > > > ------------------------- > cuncta stricte discussurus > ------------------------- > > -----Ursprüngliche Nachricht----- > Von: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] Im > Auftrag von [EMAIL PROTECTED] > Gesendet: Friday, October 10, 2008 12:30 PM > An: r-help@r-project.org > Betreff: [R] Coefficients in a polynomial glm with family > poisson/binomial > > Dear R-users > > When running a glm polynomial model with one explanatory > variable (example > Y~X+X^2), with a poisson or binomial error distribution, > the predicted > values obtained from using the predict() function and those > obtained from > using the coefficients from the summary table "as > is" in an equation of the > form Y=INTERCEPT+ XCoef x X + XCoef x X^2, differ > considerably. The former > are correct and the latter are wrong. > This does not occur using lm() or in a glm with family as > normal. I conclude > that this is due to the link function, predict() having > some way of back > transforming the data. But if this is so, are the estimated > coefficients > wortheless in this case? > I need to get accurate coefficients (for use in another > model using offset), > and have resorted to re-estimating them by running a second > polynomial (lm() > this time) on the predicted values from predict() of the > glm. This is > clearly not a nice way of doing things. > > Could anyone please inform me of why this is happening and > of a better way > around this? > > > Code: > > glm2<-glm(FEDSTATUS1~AGE+I(AGE^2), > family=binomial(link="probit")) > summary(glm2) ### first set of "wrong > coefficients" > > nd1<-expand.grid(AGE=c(1:70)) > Pred.Fed1<-predict(glm2,nd1,type="response") > points(predict(glm2,nd1,type="response")~nd1$AGE, > col=2) > > > AGE11<-c(11:70) > Pred<-t(rbind(Pred.Fed1,AGE11)) > Pred<-as.data.frame(Pred) > model<-lm(Pred$Pred.Fed1~Pred$AGE11+I(Pred$AGE11^2)) > summary(model) ### "accurate coefficients" > > > Thanks > > Samuel Riou > University of Leeds > > > > > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, > reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
