R help - May 2008 - Plotting a cubic line from a multiple regression

Dear all,

I'm attempting to plot a cubic relationship between two variables  
controlling for the effects of a third variable. In this short  
example, I'm trying to use AGE to predict CORTEX while controlling for  
the effects of TIV (total intracranial volume):

########################
cortex = rnorm(100, mean=0.5, sd=0.5)
age = rnorm(100, mean=10, sd=2)
tiv = rnorm(100, mean=1000, sd=100)

##
## simple regression (ignoring TIV) works
##
cortex.lm = lm(cortex ~ poly(age, degree=3))
plot(age, cortex)
pseudo.x = seq(min(age)-2, max(age)+2, len=200)
lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x)))

##
## multiple regression (accounting for TIV) fails
##
cortex.lm = lm(cortex ~ poly(age, degree=3) + tiv)
plot(age, cortex)
pseudo.x = seq(min(age)-2, max(age)+2, len=200)
lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x)))
########################

Although the last 'lines' command fails, summary(cortex.lm) does give  
me reasonable coefficients for the multiple regression. Can anyone  
advise me if (1) this is at all a legitimate procedure, and (2) how to  
draw the cubic function that fits the multiple regression?

Thanks!

Ash.

-----
Ashish Ranpura
Institute of Cognitive Neuroscience
University College London
17 Queen Square
London WC1N 3AR

tel: +44 (20) 7679 1126
web: http://www.icn.ucl.ac.uk

> I'm attempting to plot a cubic relationship between two variables 
> controlling for the effects of a third variable. In this short 
> example, I'm trying to use AGE to predict CORTEX while controlling for 
> the effects of TIV (total intracranial volume):
> 
> ########################
> cortex = rnorm(100, mean=0.5, sd=0.5)
> age = rnorm(100, mean=10, sd=2)
> tiv = rnorm(100, mean=1000, sd=100)
> 
> ##
> ## simple regression (ignoring TIV) works
> ##
> cortex.lm = lm(cortex ~ poly(age, degree=3))
> plot(age, cortex)
> pseudo.x = seq(min(age)-2, max(age)+2, len=200)
> lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x)))
> 
> ##
> ## multiple regression (accounting for TIV) fails
> ##
> cortex.lm = lm(cortex ~ poly(age, degree=3) + tiv)
> plot(age, cortex)
> pseudo.x = seq(min(age)-2, max(age)+2, len=200)
> lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x)))
> ########################
> 
> Although the last 'lines' command fails, summary(cortex.lm) does
give
> me reasonable coefficients for the multiple regression. Can anyone 
> advise me if (1) this is at all a legitimate procedure, and (2) how to 
> draw the cubic function that fits the multiple regression?
The last line fails because you haven't specified any values for TIV in 
the data frame.  There are a couple of things you can plot:

1. The effect on cortex of varying x, at different levels of tiv (which is 
what you were doing)
lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x, tiv=1000)))
lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x, 
tiv=min(tiv))), col="red")
lines(pseudo.x, predict(cortex.lm, data.frame(age=pseudo.x, 
tiv=max(tiv))), col="blue")

2. The effect on cortex of varying tiv, at different levels of age.
pseudo.tiv = seq(min(tiv)-20, max(tiv)+20, len=200)
plot(tiv, cortex)
lines(pseudo.tiv, predict(cortex.lm, data.frame(age=8, tiv=pseudo.tiv)))
lines(pseudo.tiv, predict(cortex.lm, data.frame(age=min(age), 
tiv=pseudo.tiv)), col="red")
lines(pseudo.tiv, predict(cortex.lm, data.frame(age=max(age), 
tiv=pseudo.tiv)), col="blue")

Regards,
Richie.

Mathematical Sciences Unit
HSL


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Hi Ashish,

I am rather more concerned about whether what you outlined is legitimate 
(your question 1 below). If you are looking at children, higher AGE will 
be associated with higher TIV, so both variables would essentially 
measure the same thing (see Miller & Chapman, Misunderstanding Analysis 
of Covariance), which I really would not like to see.

Of course, if you are looking at adults, this will probably not apply.

Best wishes,
Stephan


Ashish Ranpura schrieb:
> 
> Dear all,
> 
> I'm attempting to plot a cubic relationship between two variables 
> controlling for the effects of a third variable. In this short example, 
> I'm trying to use AGE to predict CORTEX while controlling for the 
> effects of TIV (total intracranial volume):
(snip)
> Although the last 'lines' command fails, summary(cortex.lm) does
give me
> reasonable coefficients for the multiple regression. Can anyone advise 
> me if (1) this is at all a legitimate procedure, and (2) how to draw the 
> cubic function that fits the multiple regression?