[R] Homogeneity of regression slopes

[Michael Bedward]

Thanks for turning my half-baked suggestion into something that would
actually work Cliff :)

Michael

On 14 September 2010 12:27, Clifford Long <gnolffilc at gmail.com> wrote:
> 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