# [R] robust mlm in R?

John Fox jfox at mcmaster.ca
Tue Jun 3 21:43:54 CEST 2008

```Dear Michael,

I don't think that anyone else has suggested a fix, so here's one:

-------- snip -----------

# Mahalanobis Dsq for a matrix of variables
dsq <- function(x, Sigma) {
if (missing(Sigma)) Sigma <- cov(x, use="complete.obs")
dev <- scale(x, scale=FALSE)
# DSQ <- dev %*% solve(Sigma) %*% t(dev )
DSQ <- apply(dev * (dev %*% solve(Sigma)), 1, sum)
return(DSQ)
}

# robust mlm via multivariate trimming a la Gnanadesikan, Kettering & Wilks
rmlm.GKW <- function(formula, weights, data, iter=3, pvalue=.01, ...) {
if (missing(data)) data <- model.frame(formula)
if (missing(weights)) weights <- rep(1, nrow(data))
last.weights <- weights
for (i in 1:iter) {
data\$weights <- weights
mod <- lm(formula=formula, data=data, weights=weights, ...)
res <- residuals(mod)
coef <- mod\$coefficients
print (coef)
p <- ncol(res)
DSQ <- dsq(res)
prob <- pchisq(DSQ, p, lower.tail=FALSE)
weights <- ifelse( prob<pvalue, 0, weights)
nzero <- which(weights==0)
print (nzero)
if (isTRUE(all.equal(weights, last.weights))) { break }
}
mod
}

-------- snip -----------

There were a scoping problem in the call to lm() and some other errors as
well.

I think that this revised function does what you want, but I'd also probably
program it differently, handling the standard model arguments in the
function and calling lm.wfit() for the computations.

I hope this helps,
John

------------------------------
John Fox, Professor
Department of Sociology
McMaster University
web: socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Michael Friendly
> Sent: June-02-08 9:51 AM
> To: r-help at stat.math.ethz.ch
> Subject: Re: [R] robust mlm in R?
>
> I had no on-list replies, so I cobbled up a function for the simplest
> method I could think of -- iterative multivariate trimming, following
> Gnanadesikan, Kettering & Wilks, assigning 0 weights to observations
> based on the Mahalanobis D^2 of residuals.
>
> But I'm getting an error I don't understand, and neither traceback()
> nor browser() gives me any insight.  Can anyone tell me what is wrong
> with the lm() call in rmlm.GKW below?
>
>  > iris.rmod <- rmlm.GKW(cbind(Sepal.Length, Sepal.Width, Petal.Length,
> Petal.Width)~Species, data=iris)
> Error in model.frame.default(formula = formula, data = data, subset =
> subset,  :
>    invalid type (closure) for variable '(weights)'
>  >
>
> Here are the functions:
>
> # Mahalanobis Dsq for a matrix of variables
> dsq <- function(x, Sigma) {
>    if (missing(Sigma)) Sigma <- cov(x, use="complete.obs")
>    dev <- scale(x, scale=FALSE)
> # DSQ <- dev %*% solve(Sigma) %*% t(dev )
>    DSQ <- apply(dev * (dev %*% solve(Sigma)), 1, sum)
>    return(DSQ)
> }
>
> # robust mlm via multivariate trimming a la Gnanadesikan, Kettering &
Wilks
> rmlm.GKW <- function(formula, data, subset, weights=NULL, iter=3,
> pvalue=.01) {
>    if (missing(weights) | is.null(weights)) { weights <- rep(1,
> nrow(data)) }
>    last.weights <- weights
>    for (i in 1:iter) {
>      mod <- lm(formula=formula, data=data, subset=subset, weights=weights)
>      res <- residuals(mod)
>      coef <- mod\$coefficients
>      print (coef)
>      p <- ncol(res)
>      DSQ <- dsq(res)
>      prob <- pchisq(DSQ, p, lower.tail=FALSE)
>      weights <- ifelse( prob<pvalue, 0, weights)
>      nzero <- which(weights=0)
>      print (nzero)
>      if (all.equal(weights, last.weights)) { break }
>    }
> }
>
> Michael Friendly wrote:
> > I'm looking for something in R to fit a multivariate linear model
> > robustly, using
> > an M-estimator or any of the myriad of other robust methods for linear
> > models
> > implemented in robustbase or methods based on MCD or MVE covariance
> > estimation (package rrcov).
> >
> > E.g., one can fit an mlm for the iris data as:
> > iris.mod <- lm(cbind(Sepal.Length, Sepal.Width, Petal.Length,
> > Petal.Width) ~ Species, data=iris)
> >
> > What I'd like is something like rlm() in MASS, but handling an mlm,
e.g.,
> > iris.mod <- rmlm(cbind(Sepal.Length, Sepal.Width, Petal.Length,
> > Petal.Width) ~ Species, data=iris)
> > and returning a vector of observation weights in its result.
> >
> > There's a burgeoning literature on this topic, but I haven't yet found
> > computational methods.
> > Any pointers or suggestions would be appreciated.
> >
> > -Michael
> >
> >
>
>
> --
> Michael Friendly     Email: friendly AT yorku DOT ca
> Professor, Psychology Dept.
> York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
> 4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html
> Toronto, ONT  M3J 1P3 CANADA
>
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```