[Fwd: Re: Parameterization puzzle]
Bother! This cold has made me accident-prone. I meant to hit Reply-all.
Clarification below.
-------- Original Message --------
Subject: Re: [R] Parameterization puzzle
Date: Fri, 21 Jul 2006 19:10:03 +1200
From: Murray Jorgensen <maj at waikato.ac.nz>
To: Prof Brian Ripley <ripley at stats.ox.ac.uk>
References: <44C063E5.3020703 at waikato.ac.nz>
<Pine.LNX.4.64.0607210716270.12611 at gannet.stats.ox.ac.uk>
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 at 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 at waikato.ac.nz Fax 7 838 4155 Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 1395 862