# [R] robust mlm in R?

Michael Friendly friendly at yorku.ca
Mon Jun 2 15:51:15 CEST 2008

```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