# [R] Parameterization puzzle

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

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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