Joao,
Your intuition is correct, the intercept represents the predicted value
for wool A and tension L. But, you're tripping up on how to figure out
that predicted value. In the model that you fit, the predicted value for
wool A and tension L is not simply the mean of the observations for wool A
and tension L, because there are only main effects in the model (no
interaction). Try this:
attach(warpbreaks)
tapply(breaks, list(wool, tension), mean)
fit <- lm(breaks ~ wool + tension, data=warpbreaks)
tapply(fit$fitted, list(wool, tension), mean)
fit2 <- lm(breaks ~ wool*tension, data=warpbreaks)
tapply(fit2$fitted, list(wool, tension), mean)
I believe that your results will depend on how the "contrasts" option is
set in R. For me it's like this:
options("contrasts")
$contrasts
unordered ordered
"contr.treatment" "contr.poly"
Jean
Joao Azevedo <joao.c.azev...@gmail.com> wrote on 07/27/2012 07:16:10 AM:
>
> Hi!
>
> Thanks for the link. I've already stumbled upon that explanation. I'm
> able to understand how the coding schemes are applied in the supplied
> examples, but they only use a single explanatory variable. My problem
> is with understanding the model when there are multiple categorical
> explanatory variables.
>
> --
> Joao.
>
> On Fri, Jul 27, 2012 at 1:04 PM, Jean V Adams <jvad...@usgs.gov> wrote:
> > Joao,
> >
> > There's a very thorough explanation at
> > http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
> >
> > Jean
> >
> >
> > Joao Azevedo <joao.c.azev...@gmail.com> wrote on 07/27/2012 06:32:31
AM:
> >
> >>
> >> Hi!
> >>
> >> I'm failing to understand the value of the intercept value in a
> >> multiple linear regression with categorical values. Taking the
> >> "warpbreaks" data set as an example, when I do:
> >>
> >> > lm(breaks ~ wool, data=warpbreaks)
> >>
> >> Call:
> >> lm(formula = breaks ~ wool, data = warpbreaks)
> >>
> >> Coefficients:
> >> (Intercept) woolB
> >> 31.037 -5.778
> >>
> >> I'm able to understand that the value of intercept is the mean value
> >> of breaks when wool equals "A", and that adding up the "woolB"
> >> coefficient to the intercept value I get the mean value of breaks
when
> >> wool equals "B". However, if I also consider the tension variable in
> >> the model, I'm unable to figure out the meaning of the intercept
> >> value:
> >>
> >> > lm(breaks ~ wool + tension, data=warpbreaks)
> >>
> >> Call:
> >> lm(formula = breaks ~ wool + tension, data = warpbreaks)
> >>
> >> Coefficients:
> >> (Intercept) woolB tensionM tensionH
> >> 39.278 -5.778 -10.000 -14.722
> >>
> >> I thought it would be the mean value of breaks when either wool
equals
> >> "A" or tension equals "L", but that isn't true for this dataset.
> >>
> >> Any clues on interpreting the value of intercept?
> >>
> >> Thanks!
> >>
> >> --
> >> Joao.
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