On Wednesday 01 February 2006 02:37, maneesh deshpande
wrote:> Hi,
>
> I have a data set with a continuous predictor X, a factor
> A and a continuous dependent
> variable Y.
> I am trying to build a linear model of the form:
>
> Y = (b0 + b1*X1)*B(A)
>
> where B(A) is a constant for each level of the factor A.
> I am not quite sure how to formulate the appropriate
> model formula. If I write:
>
> Y ~ ( 1 + X)/A
>
> , I get estimates for as many constants and slopes as the
> number of levels of A.
Yes, that's right: the / symbol has a special
(non-arithmetic) meaning when used like this in a model
formula. See for example p151 onwards in the reference
that is given by ?formula.
> What I really need is an overall multiplicative constant
> which depends on the factor A.
The gnm (generalized nonlinear models) package has
facilities for this. The model above could be specified
there as
Y ~ -1 + Mult(X, -1 + A)
(where the first "-1" removes the intercept, and the second
one says to estimate a separate multiplier for each level
of A rather than using contrasts in A). Or, if you want to
constrain all of your multipliers to have the same sign,
you can use
Y ~ -1 + Mult(X, Exp(-1 + A))
(note the capital E there!).
It is unclear to me that using the *same* set of multipliers
for both intercept and slope will typically be the right
thing to do, though. It would not, for example, be
invariant to transformation of X to X-c, with c constant.
That is to say, your X variable needs to be on a scale for
which the zero value has a special meaning, in order to
allow the above model to make sense. But presumably you
have thought about this already.
Hoping that helps,
David
--
Professor David Firth
http://www.warwick.ac.uk/go/dfirth