wle.lm {wle} | R Documentation |
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.
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)
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. |
num.sol |
maximum number of roots to be searched. |
raf |
type of Residual adjustment function to be use:
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 . |
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
.
wle.lm
returns an object of class
"wle.lm"
.
The function summary
is used to obtain and print a summary of the results.
The generic accessor functions coefficients
, residuals
and fitted.values
extract coefficients, residuals and fitted values returned by wle.lm
.
The object returned by wle.lm
are:
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. |
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 imax iteration 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. |
Claudio Agostinelli
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.
wle.smooth an algorithm to choose the smoothing parameter for normal distribution and normal kernel.
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)