[R] Alternatives to linear regression with multiple variables

[David Winsemius]

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
> -- 
> View this message in context: http://n4.nabble.com/Alternatives-to-linear-regression-with-multiple-variables-tp1564370p1564370.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
Heritage Laboratories
West Hartford, CT