[R] Advice on picking a regression method

[Vito Ricci]

Dear Thomas,

I believe a GLS (Generalized Least Squares, known also
as Aitken estimator) estimate could be used in case of
heteroskedasticity of residuals. See:

? lm.gls  in MASS package or ? gls in nlme package

Another way is to study the relentionship between x
(indipendent variable) and the variance of y
(dependent variable) usig a graphic. I read, when I
was a student, there some transformation which can
reduce heteroskedasticity , but I don't remember
particulars.

For theory about GLS:

http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-timeseries-regression.pdf
(here you can find some applications of GLS with R)

http://www.sinica.edu.tw/as/ssrc/ckuan/pdf/et01/ch4.pdf

http://jackman.stanford.edu/papers/gls.pdf


Best
Vito






Dear R-users,

There are tons of methods out there for fitting
independant variables to a
dependent variable. All stats books tell you about the
assumptions behind
OLS (ordinary least squares) and warn against abusive
use of the method
(which many of us do disregard by lack of a better
knowledge). Most
introductory text books stop there and don't tell you
what the next best
option might be. I am aware that there might be many
depending on the type
of study so here are the data to sort this question
out.

In this instance, I am performing a regression on
observations whose
residuals show heteroscedasticity (the variance of
residuals is small for
small dependant variable values and increases for
larger ones), which
violates one assumption of the OLS method. Which of
the numerous options
should I choose? glm, robust lm, ...

The problem is kept simple for now. I only try to
explain the log of local
topographic slope (dependent variable) with regard to
the distance to the
outlet of a catchment (independent variable) for a
fixed drained area. Both
variables are continuous.

I ordered Venables and Ripley 2002, which I suspect is
a sound reading for
advanced stats with R, but it has not arrived yet and
I need to move on
asap. Any advice or pointer to the appropriate
literature is greatly
appreciated.

Thomas

Dr Thomas Dewez
ENTEC Post-Doctoral Fellow 
ARN - MAS
BRGM (French Geological Survey)
3 Av. C. Guillemin
45000 Orleans - France

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