[Rd] NIST StRD linear regression
Martin Maechler
maechler at stat.math.ethz.ch
Mon Jul 31 09:08:58 CEST 2006
>>>>> "RobCar" == Carnell, Rob C <CarnellR at BATTELLE.ORG>
>>>>> on Sun, 30 Jul 2006 19:42:29 -0400 writes:
RobCar> NIST maintains a repository of Statistical Reference
RobCar> Datasets at http://www.itl.nist.gov/div898/strd/. I
RobCar> have been working through the datasets to compare
RobCar> R's results to their references with the hope that
RobCar> if all works well, this could become a validation
RobCar> package.
RobCar> All the linear regression datasets give results with
RobCar> some degree of accuracy except one. The NIST model
RobCar> includes 11 parameters, but R will not compute the
RobCar> estimates for all 11 parameters because it finds the
RobCar> data matrix to be singular.
RobCar> The code I used is below. Any help in getting R to
RobCar> estimate all 11 regression parameters would be
RobCar> greatly appreciated.
RobCar> I am posting this to the R-devel list since I think
RobCar> that the discussion might involve the limitations of
RobCar> platform precision.
RobCar> I am using R 2.3.1 for Windows XP.
RobCar> rm(list=ls())
RobCar> require(gsubfn)
RobCar> defaultPath <- "my path"
RobCar> data.base <- "http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA"
Here is a slight improvement {note the function file.path(); and
model <- ..; also poly(V2, 10) !}
which shows you how to tell lm() to "believe" in 10 digit
precision of input data.
-------------------------------------------------------------------------------
reg.data <- paste(data.base, "/Filip.dat", sep="")
filePath <- file.path(defaultPath, "NISTtest.dat")
download.file(reg.data, filePath, quiet=TRUE)
A <- read.table(filePath, skip=60, strip.white=TRUE)
## If you really need high-order polynomial regression in S and R,
## *DO* as you are told in all good books, and use orthogonal polynomials:
(lm.ok <- lm(V1 ~ poly(V2,10), data = A))
## and there is no problem
summary(lm.ok)
## But if you insist on doing nonsense ....
model <- "V1 ~ V2+ I(V2^2)+I(V2^3)+I(V2^4)+I(V2^5)+I(V2^6)+I(V2^7)+I(V2^8)+I(V2^9)+I(V2^10)"
## MM: "better":
(model <- paste("V1 ~ V2", paste("+ I(V2^", 2:10, ")", sep='', collapse='')))
(form <- formula(model))
mod.mat <- model.matrix(form, data = A)
dim(mod.mat) ## 82 11
(m.qr <- qr(mod.mat ))$rank # -> 10 (only, instead of 11)
(m.qr <- qr(mod.mat, tol = 1e-10))$rank # -> 11
(lm.def <- lm(form, data = A)) ## last coef. is NA
(lm.plus <- lm(form, data = A, tol = 1e-10))## no NA coefficients
-------------------------------------------------------------------------------
RobCar> reg.data <- paste(data.base, "/Filip.dat", sep="")
RobCar> model <-
RobCar> "V1~V2+I(V2^2)+I(V2^3)+I(V2^4)+I(V2^5)+I(V2^6)+I(V2^7)+I(V2^8)+I(V2^9)+I
RobCar> (V2^10)"
RobCar> filePath <- paste(defaultPath, "//NISTtest.dat", sep="")
RobCar> download.file(reg.data, filePath, quiet=TRUE)
RobCar> A <- read.table(filePath, skip=60, strip.white=TRUE)
RobCar> lm.data <- lm(formula(model), A)
RobCar> lm.data
RobCar> Rob Carnell
A propos NIST StRD:
If you go further to NONlinear regression,
and use nls(), you will see that high quality statistics
packages such as R do *NOT* always conform to NIST -- at least
not to what NIST did about 5 years ago when I last looked.
There are many nonlinear least squares problems where the
correct result is *NO CONVERGENCE* (because of
over-parametrization, ill-posednes, ...),
owever many (cr.p) pieces of software do "converge"---falsely.
I think you find more on this topic in the monograph of
Bates and Watts (1988), but in any case,
just install and use the CRAN R package 'NISTnls' by Doug Bates
which contains the data sets with documentation and example
calls.
Martin Maechler, ETH Zurich
More information about the R-devel
mailing list