R help - Apr 2013 - Polynomial Regression and NA coefficients in R

Hey all,

I'm performing polynomial regression. I'm simulating x values using
runif() and y values using a deterministic function of x and rnorm().

When I perform polynomial regression like this:

fit_poly <- lm(y ~ poly(x,11,raw = TRUE))

I get some NA coefficients. I think this is due to the high correlation between
say x and x^2 if x is distributed uniformly on the unit interval (as is the case
in my example). However, I'm still able to plot a polynomial fit like this:

points(x, predict(fit_poly), type="l", col="green", lwd=2)

What I'm interested in finding out is, how R handles the NA values I get for
some coefficients (and how that affects the polynomial I see plotted).

Thanks!

Inline.

-- Bert

On Sat, Apr 27, 2013 at 8:48 AM, Lucas Holland <hollandlucas at gmail.com>
wrote:
> Hey all,
>
> I'm performing polynomial regression. I'm simulating x values using
runif() and y values using a deterministic function of x and rnorm().
>
> When I perform polynomial regression like this:
>
> fit_poly <- lm(y ~ poly(x,11,raw = TRUE))
>
> I get some NA coefficients. I think this is due to the high correlation
between say x and x^2 if x is distributed uniformly on the unit interval (as is
the case in my example). However, I'm still able to plot a polynomial fit
like this:
>
> points(x, predict(fit_poly), type="l", col="green",
lwd=2)
>
> What I'm interested in finding out is, how R handles the NA values I
get for some coefficients (and how that affects the polynomial I see plotted).
It ignores them, i.e. treats them as 0.

You are overfitting. See the singular.ok  argument.

Incidentally, using high order polynomials as data smoothers is
nowadays usually frowned on. Consider using splines or other
effectively local smoothers instead. R has many alternatives.

-- Bert
>
> Thanks!
>
> ______________________________________________
> 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.


-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

Hi Lucas,

You may find some of these examples useful (towards the end):

http://elkhartgroup.com/rmodels.php

For example in your case you could be using b splines instead of an 11th
order polynomial, or use thin plate regression splines from the mgcv
package.  I will also humbly suggest that ggplot2 overlaying observed
values with predicted lines is a more elegant way to visualize the data and
the results.

Cheers,

Josh



On Sat, Apr 27, 2013 at 8:48 AM, Lucas Holland
<hollandlucas@gmail.com>wrote:
> Hey all,
>
> I'm performing polynomial regression. I'm simulating x values using
> runif() and y values using a deterministic function of x and rnorm().
>
> When I perform polynomial regression like this:
>
> fit_poly <- lm(y ~ poly(x,11,raw = TRUE))
>
> I get some NA coefficients. I think this is due to the high correlation
> between say x and x^2 if x is distributed uniformly on the unit interval
> (as is the case in my example). However, I'm still able to plot a
> polynomial fit like this:
>
> points(x, predict(fit_poly), type="l", col="green",
lwd=2)
>
> What I'm interested in finding out is, how R handles the NA values I
get
> for some coefficients (and how that affects the polynomial I see plotted).
>
> Thanks!
>
> ______________________________________________
> R-help@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.
>


-- 
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://joshuawiley.com/
Senior Analyst - Elkhart Group Ltd.
http://elkhartgroup.com

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