# [R] Re : AW: Coefficients in a polynomial glm with family poisson/binomial

sam_oi at yahoo.fr sam_oi at yahoo.fr
Sat Oct 11 12:17:51 CEST 2008

```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 <daniel at umd.edu> a écrit :

> De: Daniel Malter <daniel at umd.edu>
> Objet: AW: [R] Coefficients in a polynomial glm with family poisson/binomial
> À: sam_oi at yahoo.fr, r-help at 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: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] Im
> Auftrag von sam_oi at yahoo.fr
> Gesendet: Friday, October 10, 2008 12:30 PM
> An: r-help at 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),
> 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
>
>
>
>
>
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