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Last data update: 2014.03.03

R: Rank-based Estimates of Regression Coefficients

rfit	R Documentation

Rank-based Estimates of Regression Coefficients

Description

Minimizes Jaeckel's dispersion function to obtain a rank-based solution for linear models.

Usage

rfit(formula, data = list(), ...)

## Default S3 method:
rfit(formula, data, subset, yhat0 = NULL, 
scores = Rfit::wscores, symmetric = FALSE, TAU = "F0", ...)

Arguments

`formula`	an object of class formula
`data`	an optional data frame
`subset`	an optional argument specifying the subset of observations to be used
`yhat0`	an n by vector of initial fitted values, default is NULL
`scores`	an object of class 'scores'
`symmetric`	logical. If 'FALSE' uses median of residuals as estimate of intercept
`TAU`	version of estimation routine for scale parameter. F0 for Fortran, R for (slower) R, N for none
`...`	additional arguments to be passed to fitting routines

Details

Rank-based estimation involves replacing the L2 norm of least squares estimation with a pseudo-norm which is a function of the ranks of the residuals. That is, in rank estimation, the usual notion of Euclidean distance is replaced with another measure of distance which is referred to as Jaeckel's (1972) dispersion function. Jaeckel's dispersion function depends on a score function and a library of commonly used score functions is included. e.g. Wilcoxon and sign score functions. If an inital fit is not supplied (i.e. yhat0 = NULL) then inital fit is based on an L1 fit via rq.

Value

`coefficients`	estimated regression coefficents with intercept
`residuals`	the residuals, i.e. y-yhat
`fitted.values`	yhat = x betahat

`xc`	centered design matrix
`tauhat`	estimated value of the scale parameter tau
`taushat`	estimated value of the scale parameter tau_s

`betahat`	estimated regression coefficents
`call`	Call to the function

Author(s)

John Kloke kloke@biostat.wisc.edu

References

Hettmansperger, T.P. and McKean J.W. (2011), Robust Nonparametric Statistical Methods, 2nd ed., New York: Chapman-Hall.

Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of residuals. Annals of Mathematical Statistics, 43, 1449 - 1458.

Jureckova, J. (1971). Nonparametric estimate of regression coefficients. Annals of Mathematical Statistics, 42, 1328 - 1338.

Examples

data(baseball)
data(wscores)
fit<-rfit(weight~height,data=baseball)
summary(fit)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(Rfit)
Loading required package: quantreg
Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

    backsolve

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Rfit/rfit.Rd_%03d_medium.png", width=480, height=480)
> ### Name: rfit
> ### Title: Rank-based Estimates of Regression Coefficients
> ### Aliases: rfit rfit.default
> ### Keywords: nonparametric robust regression
> 
> ### ** Examples
> 
> data(baseball)
> data(wscores)
> fit<-rfit(weight~height,data=baseball)
> summary(fit)
Call:
rfit.default(formula = weight ~ height, data = baseball)

Coefficients:
              Estimate Std. Error t.value   p.value    
(Intercept) -228.57144   56.14659 -4.0710  0.000146 ***
height         5.71429    0.76018  7.5171 4.373e-10 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Multiple R-squared (Robust): 0.4418605 
Reduction in Dispersion Test: 45.125 p-value: 0 

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>