On Feb 22, 2010, at 7:46 AM, Guy Green wrote:
I wonder if someone can give some pointers on alternatives to linear
regression (e.g. Loess) when dealing with multiple variables.
Taking any simple table with three variables, you can very easily
get the
intercept and coefficients with:
summary(lm(read_table))
For obvious reasons, the coefficients in a multiple regression are
quite
different from what you get if you calculate regressions for the
single
variables separately. Alternative approaches such as Loess seem
straightforward when you have only one variable, and have the
advantage that
they can cope even if the relationship is not linear.
My question is: how can you extend a flexible approach like Loess to a
multi-variable scenario? I assume that any non-parametric calculation
becomes very resource-intensive very quickly. Can anyone suggest
alternatives (preferably R-based) that cope with multiple variables,
even
when the relationship (linear, etc) is not known in advance?
Frank Harrell illustrates several methods for appropriate
consideration and computation of non-linear relationships in a
regression framework. His book "Regression Modeling Strategies" has
been uniformly praised by the people to whom I have recommended it. At
one point he compares graphically the effect measures using a 2-d
loess fit to that achieved with a crossed regression spline approach.
Another text that demonstrates R-implemented multiple dimensional non-
(or semi-)parametric regression approaches is Simon Wood's
"Generalized Linear Models". I have less experience with the methods
in that text, but hope to increase my familiarity in the future, since
it would extend the types of models I would have access to.
And Andy has mentioned "Local Regression and Likelihood" by Loader,
which if you use Bookfinder.com will save you $30 off the $90 price in
Amazon at the moment. (No financial interests to declare.)
I surnise that the geospatial applications are of necessity dealing
with 2 and 3 dimensional data arrangements so you might took at their
Task View and mailing list archive for worked examples and advice.
--
David
Thanks,
Guy
--
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David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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