Type: Package
Title: M-Estimators for Generalized Ratio and Linear Regression Models
Version: 0.1.0
Author: Kazumi Wada ORCID iD [aut, cre]
Maintainer: Kazumi Wada <kazwd2008@gmail.com>
Description: Robust estimators for generalized ratio model (Wada, Sakashita and Tsubaki, 2021)<doi:10.17713/ajs.v50i1.994> and linear regression model by the IRLS(iterative reweighted least squares) algorithm are contained.
License: GPL (≥ 3)
URL: <https://github.com/kazwd2008/robRatio>
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: stats
Suggests: knitr, MASS, rmarkdown, testthat (≥ 3.0.0), latex2exp, RColorBrewer
Config/testthat/edition: 3
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2025-09-12 07:44:47 UTC; wada
Repository: CRAN
Date/Publication: 2025-09-17 10:20:02 UTC

Robust estimator for the linear regression model with Huber's weight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm

Description

Robust estimator for the linear regression model with Huber's weight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm

Usage

Hirls.aad(
  x1,
  y1,
  rt = rep(1, length(y1)),
  c1 = 1.15,
  rp.max = 150,
  cg.rt = 0.01
)

Arguments

x1

explanatory variable(s)

y1

objective variable

rt

sample weights

c1

tuning parameter from 1.15 to 2.30 for the scale parameter of AAD(Average Absolute Deviation)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

HB

results of robust regression

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

Robust estimator for the linear regression model with Huber's weight function and MAD scal by iteratively re-weighted least squares (IRLS) algorithm

Description

Robust estimator for the linear regression model with Huber's weight function and MAD scal by iteratively re-weighted least squares (IRLS) algorithm

Usage

Hirls.mad(
  x1,
  y1,
  rt = rep(1, length(y1)),
  c1 = 1.44,
  rp.max = 150,
  cg.rt = 0.01
)

Arguments

x1

explanatory variable(s)

y1

objective variable

rt

sample weights

c1

tuning parameter from 1.44 to 2.88 for the scale parameter of MAD(Median Absolute Deviation)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

HB

results of robust regression

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

Robust estimator for a generalized ratio model with Huber's weight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Description

Robust estimator for a generalized ratio model with Huber's weight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Usage

RrH.aad(x1, y1, g1 = 0.5, c1 = 2.3, rp.max = 100, cg.rt = 0.01)

Arguments

x1

single explanatory variable

y1

objective variable

g1

power (default: g1=0.5(conventional ratio model))

c1

tuning parameter usually from 1.15 to 2.30 (smaller figure is more robust)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

par

robustly estimated ratio of y1 to x1

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

efg

error flag. 1: acalculia (all weights become zero) 0: successful termination

Robust estimator for a generalized ratio model with Huber's weight function and MAD scal by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Description

Robust estimator for a generalized ratio model with Huber's weight function and MAD scal by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Usage

RrH.mad(x1, y1, g1 = 0.5, c1 = 2.88, rp.max = 100, cg.rt = 0.01)

Arguments

x1

single explanatory variable

y1

objective variable

g1

power (default: g1=0.5(conventional ratio model))

c1

tuning parameter usually from 1.44 to 2.88 (equivalent to those for AAD scale)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

par

robustly estimated ratio of y1 to x1

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

efg

error flag. 1: acalculia (all weights become zero) 0: successful termination

Robust estimator for a generalized ratio model with Tukey biweight function and AAD scale by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Description

Robust estimator for a generalized ratio model with Tukey biweight function and AAD scale by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Usage

RrT.aad(x1, y1, g1 = 0.5, c1 = 8, rp.max = 100, cg.rt = 0.01)

Arguments

x1

single explanatory variable

y1

objective variable

g1

power (default: g1=0.5(conventional ratio model))

c1

tuning parameter usually from 4 to 8 (smaller figure is more robust)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

par

robustly estimated ratio of y1 to x1

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

efg

error flag. 1: acalculia (all weights become zero) 0: successful termination

Robust estimator for a generalized ratio model with Tukey biweight function and MAD scale by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Description

Robust estimator for a generalized ratio model with Tukey biweight function and MAD scale by iteratively re-weighted least squares (IRLS) algorithm for M-estimation

Usage

RrT.mad(x1, y1, g1 = 0.5, c1 = 10.03, rp.max = 100, cg.rt = 0.01)

Arguments

x1

single explanatory variable

y1

objective variable

g1

power (default: g1=0.5(conventional ratio model))

c1

tuning parameter usually from 5.01 to 10.03 (equivalent to those for AAD scale)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

par

robustly estimated ratio of y1 to x1

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

s1

changes of the scale (AAD or MAD)

efg

error flag. 1: acalculia (all weights become zero) 0: successful termination

Robust estimator for the linear regression model with Tukey's biweight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm

Description

Robust estimator for the linear regression model with Tukey's biweight function and AAD scal by iteratively re-weighted least squares (IRLS) algorithm

Usage

Tirls.aad(x1, y1, rt = rep(1, length(y1)), c1 = 8, rp.max = 150, cg.rt = 0.01)

Arguments

x1

explanatory variable(s)

y1

objective variable

rt

sample weights

c1

tuning parameter from 4 to 8 for the scale parameter of AAD(Average Absolute Deviation)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

TK

results of robust regression

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

Robust estimator for the linear regression model with Tukey's biweight function and MAD scale by iteratively re-weighted least squares (IRLS) algorithm

Description

Robust estimator for the linear regression model with Tukey's biweight function and MAD scale by iteratively re-weighted least squares (IRLS) algorithm

Usage

Tirls.mad(
  x1,
  y1,
  rt = rep(1, length(y1)),
  c1 = 10.03,
  rp.max = 150,
  cg.rt = 0.01
)

Arguments

x1

explanatory variable(s)

y1

objective variable

rt

sample weights

c1

tuning parameter from 5.01 to 10.03 for the scale parameter of MAD(Median Absolute Deviation)

rp.max

maximum number of iteration

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

TK

results of robust regression

wt

robust weights

rp

total number of iteration

s1

changes in scale through iterative calculation

Robust estimator for a generalized ratio model

Description

This function simultaneously estimates two parameters of the generalized ratio model doi:10.17713/ajs.v50i1.994. It uses Tukey's biweight function and AAD for scale of quasi residuals.

This robGR function simultaneously estimate two parameters of the generalized ratio model. It uses Tukey's biweight function and AAD for scale of quasi residuals.

Usage

robGR(x1, y1, g1 = 0, c1 = 8, rp.max = 100, cg.rt = 0.001)

robGR(x1, y1, g1 = 0, c1 = 8, rp.max = 100, cg.rt = 0.001)

Arguments

x1

single explanatory variable (a vector)

y1

objective variable to be imputed (a vector)

g1

initial gamma value (default g1=0.5)

c1

tuning constant for Tukey's biweight function. Supposed to choose 4 to 8. Smaller figure is more robust (default tp=8).

rp.max

maximum number of iteration (default: rp.max=50)

cg.rt

convergence condition to stop iteration (default: cg.rt=0.001)

Value

a list with the following elements

par

robustly estimated ratio of y1 to x1 (beta)

g1

robustly estimated power (gamma)

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

efg

error flag. 1: calculation not coverged, 0: successful termination

rt.cg

change of par(beta)

g1.cg

changes of g1(gamma)

s1.cg

changes of the scale(AAD)

a list with the following elements

par

robustly estimated ratio of y1 to x1 (beta)

g1

robustly estimated power (gamma)

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

efg

error flag. 1: calculation not coverged, 0: successful termination

rt.cg

change of par(beta)

g1.cg

changes of g1(gamma)

s1.cg

changes of the scale(AAD)

Robust estimator for ratio models

Description

This function integrates 4 functions (RrT.aad, RrT.mad, RrH.aad and RrH.mad) for estimating generalized ratio model. Please note that the values for the tuning parameter tp allowed in this function is standardized. See the vignette for the detail.

Usage

robRatio(
  x1,
  y1,
  gm = "b",
  wf = "T",
  scale = "AAD",
  rt = 1,
  tp = 8,
  rp.max = 100,
  cg.rt = 0.01
)

Arguments

x1

single explanatory variable (a vector)

y1

objective variable to be imputed (a vector)

gm

indication of gamma value as follows:
gm="a": gamma=1
gm="b": gamma=1/2 (conventional ratio model)
gm="c"; gamma=0 (regression model without intercept)

wf

weight function (wf=T : Tukey, wf=H : Huber)

scale

scale for residuals. "AAD"(default) or "MAD".

rt

sample weight (default 1)

tp

standardized tuning parameter. choose 4, 6 or 8. Smaller figure is more robust (default tp=8). See details.

rp.max

maximum number of iteration (default: rp.max=50)

cg.rt

convergence condition to stop iteration (default: cg1=0.001)

Value

a list with the following elements

cond

Weight function, scale, and other arguments choosed

par

robustly estimated ratio of y1 to x1 (beta)

res

homoscedastic quasi-residuals

wt

robust weights

rp

total number of iteration

s1

changes of the scale (AAD or MAD)

efg

error flag. 1: acalculia (all weights become zero) 0: successful termination

Examples

require(robRatio)

x1 <- seq(1, 10, by=0.1)
#e <- rnorm(length(x1))
e <- rt(length(x1), df=3)   # error term following t distribution

b <- 2		# true value of slope

y1 <- b*x1 + x1*e			# example 1: gamma=1
y2 <- b*x1 + sqrt(x1)*e   # example 2: gamma=1/2

o1 <- robRatio(x1, y1, gm="a")
o2 <- robRatio(x1, y2, gm="b")

o1$par;  o2$par     # estimated slope

cols = RColorBrewer::brewer.pal(11, "PiYG")
cl1 <- round((o1$wt)*10+1)
cl2 <- round((o2$wt)*10+1)

oldpar <- par(mfrow=c(1,2))
plot(x1, y1, col=cols[cl1], pch=20)
plot(x1, y2, col=cols[cl2], pch=20)
par(oldpar)

[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)