Re: determining contributions to a function

From: Lance Lamboy (lance.lamboy_at_lamboy.nospam.com)
Date: 06/01/04 

Date: Tue, 01 Jun 2004 09:32:09 -0400

On Mon, 31 May 2004 20:10:22 -0400, Rajarshi Guha wrote:

> Hello,
> (I'm not sure whether this is the right group to post this question so
> if its not sorry.)
>
> If I have a function of several variables, say f(x,y,z). For given
> values of x,y and z is there a way to determine the contribution to the
> value of f(x,y,z)? And similarly for y and z?
>
> The reason behind this is that if f is defined as:
>
> f(x,y,z) = x + y + z
>
> then it would be possible to say that x contributes
>
> x / f(x,y,z)
>
> to the final value and similarly for y and z.
>
> However I don't think this would be correct for any other form of f (but
> I may be wrong). In such a case is there a general way to determine
> contributions of a specific variable to the value of a function of that
> variable (and other variables)?
>
> Thanks,

First I would determine if the effects are independent. In your example,
the effects are clearly independent and I can say that x contributes x/3
to f(x,y,z). It does not matter what y and z are.

If the effects are not independent, then is the size of the possible
values of y and z small, large, countably infinite, uncountably infinite.

If the size of the possible effects of y and z are small (say y is gender
and z is marital status) then you should make a contingency table showing
the effects of x for all the possible y and z.

If the size of the possible y and z are not small, then it becomes
trickier. Prepare a contingency table with a carefully chosen small
subset of y and z.

Lance Lamboy

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