robReg: [Robust estimator for regression models

In robRatio: M-Estimators for Generalized Ratio and Linear Regression Models

[Robust estimator for regression models

Description

This function is for Robust regression by the IRLS algorithm. It integrates child functions contained in Tirls.r and Hirls.r.

Usage

robReg(
  x1,
  y1,
  wf = "T",
  scale = "AAD",
  rt = rep(1, length(y1)),
  tp = 8,
  rp.max = 150,
  cg.rt = 0.01
)

Arguments

x1	explanatory variable in regression (a vector or a matrix)
y1	objective variable in regression (a vector)
wf	weight function ("T" for Tukey's biweight, and "H" for Huber weight)
scale	scale for residuals. "AAD"(default) or "MAD".
rt	sample weight (default 1)
tp	tuning parameter (tp=4, 6 or 8) for weight function. Smaller figure is more robust.
rp.max	The maximum number of iteration (default 150)
cg.rt	convergence condition to stop iteration (default: cg.rt=0.001)

Value

a list with the following elements

cond

Weight function, scale, and other arguments choosed

TK

robustly estimated regression coefficients using Tukey's biweight

HB

robustly estimated regression coefficients using Huber weight

wt

final robust weights

rp

total number of iteration

s1

iterative changes in the sclae of residuals (AAD or MAD)

Examples

require(robRatio)

set.seed(4)
cov1 <- matrix(c(3, 2.8, 2.8, 3), 2, 2)
cov2 <- matrix(c(2.5, 0, 0, 3), 2, 2)
dat1 <-  MASS::mvrnorm(n=400, mu=c(100, 100), Sigma=cov1, empirical=TRUE)
dat2 <-  cbind(runif(100,  min=96, max=104),  runif(50,  min=95, max=105))
dat3 <- matrix(c(103, 103.5, 104.5, 104.8, 96, 98, 94, 95), 4, 2) 
dat <- rbind(dat1, dat2, dat3)
plot(dat)
y1 <- dat[,2]
x1 <- dat[,1]

R0  <- lm(y1~x1)        # regression by OLS                                         

o1 <- robReg(x1, y1, tp=4)  # robust regression by IRLS (more robust)
o2 <- robReg(x1, y1, tp=8)  # robust regression by IRLS (less robust)

oldpar <- par(mfrow=c(2,2))

# non-robust regression
  plot(dat, pch=20, main="non-robust regression")
  abline(R0, col="red", lwd=2)

# robust regression with coloring robust weight
  f.o1 <- rep(1, length(x1))
  f.o1[which(o1$wt < 0.8)] <- 3
  f.o1[which(o1$wt < 0.5)] <- 7
  f.o1[which(o1$wt < 0.2)] <- 2
  f.o1[which(o1$wt == 0)] <- 8

  plot(x1, y1, pch=20, col=f.o1)
  abline(R0, col="red", lty=3)
  abline(o1$TK, col="blue", lwd=2)
  abline(o2$TK, col="cyan", lwd=2)

# robust weights (more robust)
  hist(o1$wt, main="tp=4(more robust)")

# robust weights (less robust)
  hist(o2$wt, main="tp=4(less robust)")

par(oldpar)

robRatio documentation built on Nov. 5, 2025, 5:25 p.m.