R^2 in NLS...non-sense??
- From: Landini <my.address.is@xxxxxxxxx>
- Date: Fri, 25 Nov 2005 14:03:48 +0100
Dear all
i would like to ask to you about possibility to compare 2 different regression
models. I know that is statistically lawful make an anova on two different
model BUT only if they are fitted on the same data, while i've many (fruit
growth) models fitted on two kind of data (treated fruits vs. untreated
fruits).
In "R" with nonlinear least square is simple obtain parameter values and RSS
(residual sum square) but none R^2 coefficient is returned, in Axum 5.0A R^2
is returned. R-help list answer me that...
..............................................................................................................
For linear regression we have the following identity
total SS = regression SS + residual SS (*)
where total SS is the sum of squares of observations around their mean,
i.e.
total SS = (n-1)*var(y)
and residual SS is given by the deviance function.
R-squared is defined as
R^2 = regression SS/ total SS = 1 - residual SS/total SS.
You can use this last formula to define a similar quantity for nonlinear
regression. You have to remember that R^2 does not have its usual meaning
for NLS. In fact, the basic identity (*) does not hold and the residuals
do not add up to zero.
Hope this helps,
Andy
..............................................................................................................
So, does anybody have idea how to compare two fitted models on different data?
quantile-quantile plot of RSS's of NT vs TRT???
tnx in advance
-------------------------------------------------------------------------------------------------------------------------
Landini dr. Massimiliano
Tel. mob. (+39) 347 140 11 94
Tel./Fax. (+39) 051 762 196
e-mail: robfleming (at) tiscali (dot) it
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