# [R] newbie problem using Design.rcs

sp to_rent_2000 at yahoo.com
Tue Dec 23 22:51:12 CET 2008

```Sincere thanks for both the replies.

0. I agree, I'm waiting for my copy of a regression book to arrive. Meanwhile, I'm trying to read on google.

1. My bad, I'm using Gaussian noise.

2. I didn't have x^3 b/c that co-efficient happens to be zero in this fitting.

3. I used lines() b/c I wanted to superimpose the curve from regression atop my first plot of the original data points (x,y).
I'm not sure how to use plot(f, x1 = NA) after my first plot(). The examples I managed to find on google all use plot() followed by lines(). [In Matlab, I'd just say "hold" in between these calls.]

Also, I'm forced to call win.graph() before my first plot() to see the first plot. Is that normal?

4. I really could use some guidance on this part. I need to use rcs() to fit points in a high-dimensional space and I'm trying to understand and use it correctly.

I started with testing it on just x,y dimensions so that I can visually evaluate the fitting. I tried y=x, y=x^2 etc, adding Gaussian noise each time (to the y).

I plot original x,y and x,y' where y' is calculated using the co-efficients returned by rcs. I find that the regression curve differs from the actual points by as high as 10^5 with 3 knots and roughly -10^5 with 4 knots as I make y=x^2, y=x^3....

If this is NOT a good way to test fitting, could you pls tell me a better way?

Respectfully,
sp

--- On Tue, 12/23/08, Frank E Harrell Jr <f.harrell at vanderbilt.edu> wrote:

> From: Frank E Harrell Jr <f.harrell at vanderbilt.edu>
> Subject: Re: [R] newbie problem using Design.rcs
> To: "David Winsemius" <dwinsemius at comcast.net>
> Cc: to_rent_2000 at yahoo.com, r-help at r-project.org
> Date: Tuesday, December 23, 2008, 9:41 AM
> that your problems seem to be statistical and not
> programming ones.  I recommend that you spend a significant
> amount of time with a good regression text or course before
> using the software.  Also, with Design you can find out the
> algebraic form of the fit:
>
> f <- ols(y ~ rcs(x,3), data=mydata)
> Function(f)
>
> Frank
>
>
> David Winsemius wrote:
> >
> > On Dec 22, 2008, at 11:38 PM, sp wrote:
> >
> >> Hi,
> >>
> >> I read data from a file. I'm trying to
> understand how to use Design.rcs by using simple test data
> first. I use 1000 integer values (1,...,1000) for x (the
> predictor) with some noise (x+.02*x) and I set the response
> variable y=x. Then, I try rcs and ols as follows:
> >>
> > Not sure what sort of noise that is.
> >
> >> m = ( sqrt(y1) ~ ( rcs(x1,3) ) ); #I tried without
> sqrt also
> >> f = ols(m, data=data_train.df);
> >> print(f);
> >>
> >> [I plot original x1,y1 vectors and the regression
> as in
> >> y <- coef2[1] + coef2[2]*x1 + coef2[3]*x1*x1]
> >
> > That does not look as though it would capture the
> structure of a restricted **cubic** spline. The usual method
> in Design for plotting a model prediction would be:
> >
> > plot(f, x1 = NA)
> >
> >>
> >>
> >> But this gives me a VERY bad fit:
> >> "
> >
> > Can you give some hint why you consider this to be a
> "VERY bad fit"? It appears a rather good fit to
> me, despite the test case apparently not being construct
> with any curvature which is what the rcs modeling strategy
> should be detecting.
> >
>
>
> -- Frank E Harrell Jr   Professor and Chair
> School of Medicine
>                      Department of Biostatistics
> Vanderbilt University

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