I asked, "Do cont*cont interactions make sense?" and David Moore and
Constantine Daskalakis responded (quoted below). With respect, I think
both of them miss the distinction between having a mathematical function
and having a model that usefully describes and helps intepret a particular
dataset.
David Airey <[email protected]> provided this example looking at
eye weight in mice:
. * full model
. regress eye body* age* brain* parity* litter* sex
I [RAR] assume that:
sex is categorical;
litter [size] is discrete over a small range of values, so could be
treated as ordered categorical;
parity is place in litter [?] so could be similar;
body [length? mass?], brain [mass] and age could all be continuous.
On that interpretation, we expect eye, body and brain sizes all to be
positively correlated, and various models involving body (or body^3 if
it's length), brain, body*brain, body^2, brain^2 might give similar
goodness of fit. Size is correlated with age during the period of growth,
and there may be an argument that a young*(big for age) mouse has the
similar eye to a mature*(average size) mouse, so fitting body*age may work
mathematically.
But how much easier to interpret if one of the continuous variables is
divided into classes, so the interaction coefficient now expresses the
difference in slope of the main regression according to group membership.
The results now become plottable as a scatterplot with multiple lines.
Noting the proviso above about "correlated during the period of growth",
one might look for periods of rapid growth and compare growth rates for
the eye and body. Or one could look at a multi-stage model (SEM),
postulating that body size is a function of age, and then relate eye size
to body etc.
When I referred to an "act of faith", this was not to recommend a naive
metaphysical trust but rather to draw attention to the need to examine the
basis and usefulness of a model that somehow "represents" the science. As
I wrote, a computer will always do the arithmetic, whether or not the sum
is justified.
Allan
> At 01:02 PM 6/26/03, David E Moore wrote:
> >Let me say at the outset that I applaud any conscientious effort to
> >examine the plausibility of nonlinear and/or nonadditive models.
> >... If it's always a leap of faith to have a linear additive
> >model, then perhaps one might want to think twice about creating
> >interaction terms that assume linear relationships.
On Thu, 26 Jun 2003, Constantine Daskalakis wrote:
> I think the question has things backwards. The point of the interactions is
> that they allow us to relax model assumptions (notably, that of
> additivity). As such, they indeed make much sense -- they actually allow us
> to fit a more flexible model.
R. Allan Reese Email: [email protected]
Associate Manager GRI Direct voice: +44 1482 466845
Graduate School Voice messages: +44 1482 466844
Hull University, Hull HU6 7RX, UK. Fax: +44 1482 466436
====================================================================
The management here were SO impressed with W Edward Deming's "Out of
the crisis" that they are working flat out to create THE BEST crisis;
then they can start implementing the 13 obligations.
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
