[R] fitting non linear data
Frank E Harrell Jr
fharrell at virginia.edu
Wed May 22 15:16:34 CEST 2002
To factor in model uncertainty you might bootstrap a semiparametric regression. The Hmisc library areg.boot function, using the default method of avas, develops a semiparametric additive model and uses the bootstrap for confidence bands for the transformations on predictor and response variables. As an example I tried
f <- areg.boot(I(y) ~ x) # don't transform y, optimally transform x
# The default y ~ x shows a lot of uncertainty in transformation of y for
# large y
avas Additive Regression Model
areg.boot(x = I(y) ~ x)
n= 8 p= 1
Apparent R2 on transformed Y scale: 0.886
Bootstrap validated R2 : 0.683
Coefficients of standardized transformations:
summary.areg.boot(obj = f)
Estimates based on 100 resamples
Values to which predictors are set when estimating
effects of other predictors:
Estimates of differences of effects on Median Y (from first X value),
and bootstrap standard errors of these differences.
Settings for X are shown as row headings.
x Differences S.E Lower 0.95 Upper 0.95 Z Pr(|Z|)
3.75 0.000000 NA NA NA NA NA
5.50 -4.614057 1.268541 -7.100353 -2.127762 -3.637294 0.0002755177
7.25 -7.144868 2.030195 -11.123978 -3.165758 -3.519300 0.0004326864
plot(f) # see attached
I had to fix a small bug in the function to make this work.
In the plot, confidence bands are in black, individual bootstrap estimates are in red.
On Wed, 22 May 2002 12:21:45 +0200
gregory lefebvre <greggory.lefebvre at univ-rouen.fr> wrote:
> Hye every one,
> My question will certainly seem stupid as I am quite a beginner in R.
> I would like to trace a curve which fits these two vectors:
> x<-c( 2,3,4,5,6,7,8,10 )
> y<-c( 20, 12, 8, 6, 5, 4.5, 4, 3.8)
> It seems to follow a non linear model.
> Could anyone help me because I could'nt find the answer I am looking for
> in the FAQs.
> In advance thank you for your time.
> G. Lefebvre
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Frank E Harrell Jr Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine http://hesweb1.med.virginia.edu/biostat
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