If you'll allow me to throw in two cents ...
Like Michael said, the dummy variable route is the way to go, but I believe
that the coefficients on the dummy variables test for equal intercepts. For
equality of slopes, do we need the interaction between the dummy variable
and the explanatory variable whose slope (coefficient) is of interest? I'll
add some detail below.
For only two groups, we could use a single 2-level dummy variable D
D = 0 is the reference level (group)
D = 1 is the other level (group)
Equality of intercepts
y = b0 + b1*x + b2*D
If D = 0, then y = b0 + b1*x
If D = 1, then y = b0 + b1*x + b2 ...... group like terms: y = (b0 + b2)
+ b1*x
If coefficient b2 = 0, then we might fail to reject the null hypothesis that
the intercepts are equal
If coefficient b2 <> 0, then we would reject the null hypothesis that the
intercepts are equal
Equality of slopes model
y = b0 + b1*x + b2*D + b3*x*D
(we added the interaction between x and D)
If D = 0, then y = b0 + b1*x
If D = 1, then y = b0 + b1*x + b2 + b3*x ...... group like terms: y = (b0
+ b2) + (b1 + b3)*x
If coefficient b3 = 0, then we might fail to reject the null hypothesis that
the slopes are equal
If coefficient b3 <> 0, then we would reject the null hypothesis that
the slopes are equal
For a model with three groups, assuming that lm / glm / etc. would really do
this for you, the explicit dummy variable coding might look like:
D1 D2
group 1 0 0 (reference level ... can usually choose)
group 2 1 0
group 3 0 1
I believe that this is called a sigma-restricted model (??), as opposed to
an overparameterized model where three groups would have three dummy
variables.
You can probably find this info in most books on basic regression. This
might be overly simplistic, and I'll happily stand corrected if I've made
any mistakes.
Otherwise, I hope that this helps.
Cliff
On Mon, Sep 13, 2010 at 7:12 PM, Michael Bedward
<michael.bedw...@gmail.com>wrote:
> Hello Doug,
>
> Perhaps it would just be easier to keep your data together and have a
> single regression with a term for the grouping variable (a factor with
> 3 levels). If the groups give identical results the coefficients for
> the two non-reference grouping variable levels will include 0 in their
> confidence interval.
>
> Michael
>
>
> On 14 September 2010 06:52, Doug Adams <f...@gmx.com> wrote:
> > Hello,
> >
> > We've got a dataset with several variables, one of which we're using
> > to split the data into 3 smaller subsets. (as the variable takes 1 of
> > 3 possible values).
> >
> > There are several more variables too, many of which we're using to fit
> > regression models using lm. So I have 3 models fitted (one for each
> > subset of course), each having slope estimates for the predictor
> > variables.
> >
> > What we want to find out, though, is whether or not the overall slopes
> > for the 3 regression lines are significantly different from each
> > other. Is there a way, in R, to calculate the overall slope of each
> > line, and test whether there's homogeneity of regression slopes? (Am
> > I using that phrase in the right context -- comparing the slopes of
> > more than one regression line rather than the slopes of the predictors
> > within the same fit.)
> >
> > I hope that makes sense. We really wanted to see if the predicted
> > values at the ends of the 3 regression lines are significantly
> > different... But I'm not sure how to do the Johnson-Neyman procedure
> > in R, so I think testing for slope differences will suffice!
> >
> > Thanks to any who may be able to help!
> >
> > Doug Adams
> >
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