# Re: [R] Parameterization puzzle

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri 21 Jul 2006 - 16:20:00 EST

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@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

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Received on Fri Jul 21 16:25:09 2006

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