[R] GLM results different from GAM results without smoothing terms

[Daniel Malter]

Thanks much for your response. My apologies for not putting sample code in
the first place. Here it comes:

Round=rep(1:10,each=10)
x1=rbinom(100,1,0.3)
x2=rep(rnorm(10,0,1),each=10)

summary(glm(factor(x1)~factor(Round)+x2,family=binomial(link="probit")))

library(mgcv)
summary(gam(factor(x1)~factor(Round)+x2,family=binomial(link="probit")))

Cheers,
Daniel

-------------------------
cuncta stricte discussurus
-------------------------

-----Ursprüngliche Nachricht-----
Von: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
Gesendet: Thursday, January 03, 2008 2:13 AM
An: Daniel Malter
Cc: r-help at stat.math.ethz.ch
Betreff: Re: [R] GLM results different from GAM results without smoothing
terms

On Wed, 2 Jan 2008, Daniel Malter wrote:

> Hi, I am fitting two models, a generalized linear model and a 
> generalized additive model, to the same data. The R-Help tells that "A 
> generalized additive model (GAM) is a generalized linear model (GLM) 
> in which the linear predictor is given by a user specified sum of 
> smooth functions of the covariates plus a conventional parametric 
> component of the linear predictor." I am fitting the GAM without 
> smooth functions and would have expected the parameter estimates to be
equal to the GLM.
>
> I am fitting the following model:
>
> reg.glm=glm(YES~factor(RoundStart)+DEP+SPD+S.S+factor(LOST),family=bin
> omial(
> link="probit"))
> reg.gam=gam(YES~factor(RoundStart)+DEP+SPD+S.S+factor(LOST),family=bin
> omial(
> link="probit"))
>
> DEP, SPD, S.S, and LOST are invariant across the observations within 
> the same RoundStart. Therefore, I would expect to get NAs for these 
> parameter estimates.

So your design matrix is rank-deficient and there is an identifiability
problem.

> I get NAs in GLM, but I get estimates in GAM. Can anyone explain why 
> that is?

Because there is more than one way to handle rank deficiency.  There are two
different 'gam' functions in contributed packages for R (and none in R
itself), so we need more details: see the footer of this message.
In glm() the NA estimates are treated as zero for computing predictions.

> Thanks much,
> Daniel
>
> 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.

-- 
Brian D. Ripley,                  ripley at 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