Re: [Rd] NIST StRD linear regression

From: Martin Maechler <maechler_at_stat.math.ethz.ch>
Date: Mon 31 Jul 2006 - 07:08:58 GMT

>>>>> "RobCar" == Carnell, Rob C <CarnellR@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



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