[R] Parameterization puzzle

From: Murray Jorgensen <maj_at_waikato.ac.nz>
Date: Fri 21 Jul 2006 - 15:19:33 EST


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@waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441    Mobile 021 1395 862

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Received on Fri Jul 21 15:27:49 2006

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