wle.lm: Fitting Linear Models using Weighted Likelihood

Description

wle.lm is used to fit linear models via Weighted Likelihood, when the errors are iid from a normal distribution with null mean and unknown variance. The carriers are considered fixed. Note that this estimator is robust against the presence of bad leverage points too.

Usage

wle.lm(formula, data=list(), model=TRUE, x=FALSE,  y=FALSE, boot=30, group, num.sol=1, raf="HD",  smooth=0.031, tol=10^(-6), equal=10^(-3),  max.iter=500, contrasts=NULL, verbose=FALSE)

Arguments

formula

a symbolic description of the model to be fit. The details of model specification are given below.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which wle.lm is called from.

model, x, y

logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response.)

boot

the number of starting points based on boostrap subsamples to use in the search of the roots.

group

the dimension of the bootstap subsamples. The default value is $max(round(size/4),var)$ where $size$ is the number of observations and $var$ is the number of variables.

num.sol

maximum number of roots to be searched.

raf

type of Residual adjustment function to be used:

raf="HD": Hellinger Distance RAF,

raf="NED": Negative Exponential Disparity RAF,

raf="SCHI2": Symmetric Chi-Squared Disparity RAF.

smooth

the value of the smoothing parameter.

tol

the absolute accuracy to be used to achieve convergence of the algorithm.

equal

the absolute value for which two roots are considered the same. (This parameter must be greater than tol).

max.iter

maximum number of iterations.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

verbose

if TRUE warnings are printed.

Value

coefficients: the parameters estimator, one row vector for each root found.
standard.error: an estimation of the standard error of the parameters estimator, one row vector for each root found.
scale: an estimation of the error scale, one value for each root found.
residuals: the unweighted residuals from the estimated model, one column vector for each root found.
fitted.values: the fitted values from the estimated model, one column vector for each root found.
tot.weights: the sum of the weights divide by the number of observations, one value for each root found.
weights: the weights associated to each observation, one column vector for each root found.
f.density: the non-parametric density estimation.
m.density: the smoothed model.
delta: the Pearson residuals.
freq: the number of starting points converging to the roots.
tot.sol: the number of solutions found.
not.conv: the number of starting points that does not converge after the max.iter iterations are reached.
call: the match.call().
contrasts
xlevels
terms: the model frame.
model: if model=TRUE a matrix with first column the dependent variable and the remain column the explanatory variables for the full model.
x: if x=TRUE a matrix with the explanatory variables for the full model.
y: if y=TRUE a vector with the dependent variable.
info: not well working yet, if 0 no error occurred.

Details

Models for wle.lm are specified symbolically. A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first+second indicates all the terms in first together with all the terms in second with duplicates removed. A specification of the form first:second indicates the the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first+second+first:second.

References

Agostinelli, C., (1998) Inferenza statistica robusta basata sulla funzione di verosimiglianza pesata: alcuni sviluppi, Ph.D Thesis, Department of Statistics, University of Padova.

Agostinelli, C., Markatou, M., (1998) A one-step robust estimator for regression based on the weighted likelihood reweighting scheme, Statistics \& Probability Letters, Vol. 37, n. 4, 341-350.

Agostinelli, C., (1998) Verosimiglianza pesata nel modello di regressione lineare, XXXIX Riunione scientifica della Societ\`a Italiana di Statistica, Sorrento 1998.

Examples

Run this code

library(wle)
# You can find this data set in:
# Hawkins, D.M., Bradu, D., and Kass, G.V. (1984). 
# Location of several outliers in multiple regression data using
# elemental sets. Technometrics, 26, 197-208.
#
data(artificial)

result <- wle.lm(y.artificial~x.artificial,boot=40,num.sol=3)

summary(result)

plot(result)

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