[R] Parameterization puzzle

[Murray Jorgensen]

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
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