On Wednesday 13 February 2008, [EMAIL PROTECTED] wrote: > You ask > > When using continuous data in both Y and X, does the > difference between "raw" and "orthagonal" polynomials > have any practical meaning? > > Yes, indeed it does, even if X is not 'continuous'. There are (at > least) two practical differences: > > 1. With orthogonal polynomials you are using an orthogonal > basis, so the estimates of the regression coefficients are statistically > independent. This makes it much easier in model building to get an idea > of the degree of polynomial warranted by the data. You can usually do > it from a single model fit. > > 2. With an orthogonal polynomial basis your model matrix has, in > principle, an optimal condition number and the numerical properties of > the least squares fitting algorithm can be much better. If you really > want the raw coefficients and their standard errors, &c, you unravel > this a bit, but why would you want to? > > If all you are interested in is the fitted curve, though, (and this is > indeed the key thing, not the coefficients), then what kind of basis you > use is pretty irrelevant. > > Regards, > W.
This is exactly the kind of explanation I was looking for. Thanks! Dylan > Bill Venables > CSIRO Laboratories > PO Box 120, Cleveland, 4163 > AUSTRALIA > Office Phone (email preferred): +61 7 3826 7251 > Fax (if absolutely necessary): +61 7 3826 7304 > Mobile: +61 4 8819 4402 > Home Phone: +61 7 3286 7700 > mailto:[EMAIL PROTECTED] > http://www.cmis.csiro.au/bill.venables/ > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > On Behalf Of Dylan Beaudette > Sent: Thursday, 14 February 2008 6:42 AM > To: r-help@r-project.org > Subject: [R] use of poly() > > Hi, > > I am curious about how to interpret the results of a polynomial > regression-- > using poly(raw=TRUE) vs. poly(raw=FALSE). > > set.seed(123456) > x <- rnorm(100) > y <- jitter(1*x + 2*x^2 + 3*x^3 , 250) > plot(y ~ x) > > l.poly <- lm(y ~ poly(x, 3)) > l.poly.raw <- lm(y ~ poly(x, 3, raw=TRUE)) > > s <- seq(-3, 3, by=0.1) > > lines(s, predict(l.poly, data.frame(x=s)), col=1) > lines(s, predict(l.poly.raw, data.frame(x=s)), col=2) > > The results are the same, but the regression coeficients are different: > > as.vector(coef(l.poly)) > 1.806618 88.078858 16.194423 58.051642 > > as.vector(coef(l.poly.raw)) > -0.1025114 1.5265248 2.0617970 2.7393995 > > > When using continuous data in both Y and X, does the difference between > "raw" > and "orthagonal" polynomials have any practical meaning? > > Thanks, > > Dylan -- Dylan Beaudette Soil Resource Laboratory http://casoilresource.lawr.ucdavis.edu/ University of California at Davis 530.754.7341 ______________________________________________ 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.
