Consider the following example (based on an example in Pat Altham's GLM
notes)
pyears <- scan()
18793 52407 10673 43248 5710 28612 2585 12663 1462 5317
deaths <- scan()
2 32 12 104 28 206 28 186 31 102
Smoke <- gl(2,1,10,labels=c("No","Yes"))
Age <-
gl(5,2,10,labels=c("35-44","45-54","55-64","65-74","75-84"),
ordered=TRUE)
mod1.glm <- glm(deaths ~ Age * Smoke + offset(l),family=poisson)
summary(mod1.glm)
age <- as.numeric(Age)
mod2.glm <- aso1.glm <- glm(deaths ~ poly(age,2) + Smoke +
poly(age,1):Smoke + offset(l),family=poisson)
summary(mod2.glm)
The business part of the summary for the first model
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.92706 0.16577 -35.754 < 2e-16 ***
Age.L 4.06490 0.47414 8.573 < 2e-16 ***
Age.Q -1.08293 0.41326 -2.620 0.008781 **
Age.C 0.24158 0.31756 0.761 0.446816
Age^4 0.04244 0.23061 0.184 0.853986
SmokeYes 0.61916 0.17296 3.580 0.000344 ***
Age.L:SmokeYes -1.31234 0.49267 -2.664 0.007729 **
Age.Q:SmokeYes 0.39043 0.43008 0.908 0.363976
Age.C:SmokeYes -0.29593 0.33309 -0.888 0.374298
Age^4:SmokeYes -0.03682 0.24432 -0.151 0.880218
inspires me to fit the second model that omits the nonsignificant terms,
however this produces the summary
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.8368 0.1213 -48.103 < 2e-16 ***
poly(age, 2)1 3.9483 0.1755 22.497 < 2e-16 ***
poly(age, 2)2 -1.0460 0.1448 -7.223 5.08e-13 ***
SmokeYes 0.5183 0.1262 4.106 4.02e-05 ***
SmokeNo:poly(age, 1) 1.3755 0.4340 3.169 0.00153 **
SmokeYes:poly(age, 1) NA NA NA NA
Why do we get a SmokeNo:poly(age, 1) term? Can I re-express mod2.glm so
that this term does not appear?
Cheers, Murray Jorgensen
--
Dr Murray Jorgensen http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz Fax 7 838 4155
Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 1395 862
R does not know that poly(age,2) and poly(age,1) are linearly dependent.
(And indeed they only are for some functions 'poly'.)
I cannot reproduce your example ('l' is missing), but perhaps
glm(deaths ~ poly(age,2) + poly(age,1)*Smoke + offset(l), poisson)
was your intention?
On Fri, 21 Jul 2006, Murray Jorgensen wrote:
> Consider the following example (based on an example in Pat Altham's GLM
> notes)
>
> pyears <- scan()
> 18793 52407 10673 43248 5710 28612 2585 12663 1462 5317
>
> deaths <- scan()
> 2 32 12 104 28 206 28 186 31 102
>
> Smoke <- gl(2,1,10,labels=c("No","Yes"))
> Age <-
gl(5,2,10,labels=c("35-44","45-54","55-64","65-74","75-84"),
> ordered=TRUE)
> mod1.glm <- glm(deaths ~ Age * Smoke + offset(l),family=poisson)
> summary(mod1.glm)
> age <- as.numeric(Age)
> mod2.glm <- aso1.glm <- glm(deaths ~ poly(age,2) + Smoke +
> poly(age,1):Smoke + offset(l),family=poisson)
> summary(mod2.glm)
>
>
>
> The business part of the summary for the first model
>
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -5.92706 0.16577 -35.754 < 2e-16 ***
> Age.L 4.06490 0.47414 8.573 < 2e-16 ***
> Age.Q -1.08293 0.41326 -2.620 0.008781 **
> Age.C 0.24158 0.31756 0.761 0.446816
> Age^4 0.04244 0.23061 0.184 0.853986
> SmokeYes 0.61916 0.17296 3.580 0.000344 ***
> Age.L:SmokeYes -1.31234 0.49267 -2.664 0.007729 **
> Age.Q:SmokeYes 0.39043 0.43008 0.908 0.363976
> Age.C:SmokeYes -0.29593 0.33309 -0.888 0.374298
> Age^4:SmokeYes -0.03682 0.24432 -0.151 0.880218
>
> inspires me to fit the second model that omits the nonsignificant terms,
> however this produces the summary
>
> Estimate Std. Error z value Pr(>|z|)
> (Intercept) -5.8368 0.1213 -48.103 < 2e-16 ***
> poly(age, 2)1 3.9483 0.1755 22.497 < 2e-16 ***
> poly(age, 2)2 -1.0460 0.1448 -7.223 5.08e-13 ***
> SmokeYes 0.5183 0.1262 4.106 4.02e-05 ***
> SmokeNo:poly(age, 1) 1.3755 0.4340 3.169 0.00153 **
> SmokeYes:poly(age, 1) NA NA NA NA
>
> Why do we get a SmokeNo:poly(age, 1) term? Can I re-express mod2.glm so
> that this term does not appear?
>
> Cheers, Murray Jorgensen
>
>
--
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