# [R] [Fwd: Re: Parameterization puzzle]

From: Murray Jorgensen <maj_at_waikato.ac.nz>
Date: Fri 21 Jul 2006 - 19:58:20 EST

Bother! This cold has made me accident-prone. I meant to hit Reply-all. Clarification below.

Apologies for a non-selfcontained example. Here is what I should have sent:

pyears <- scan()
18793 52407 10673 43248 5710 28612 2585 12663 1462 5317

deaths <- scan()
2 32 12 104 28 206 28 186 31 102

l <- log(pyears)
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)

Cheers, Murray Jorgensen

Prof Brian Ripley wrote:

```> 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
>>
>>
>
```--
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

--
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 20:31:56 2006

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