wle.stepwise {wle}R Documentation

Weighted Stepwise, Backward and Forward selection methods

Description

This function performs Weighted Stepwise, Forward and Backward model selection.

Usage

wle.stepwise(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, min.weight=0.5, type="Forward", 
             f.in=4.0, f.out=4.0, method="WLE", contrasts=NULL)

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.stepwise 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.
min.weight see details.
type type="Stepwise": the weighted stepwise methods is used,
type="Forward": the weighted forward methods is used,
type="Backward": the weighted backward method is used.
f.in the in value
f.out the out value
method method="WLS": the submodel parameters are estimated by weighted least square with weights from the weighted likelihood estimator on the full model.
method="WLE": the submodel parameters are estimated by weighted likelihood estimators.
contrasts an optional list. See the contrasts.arg of model.matrix.default.

Details

Models for wle.stepwise 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.

min.weight: the weighted likelihood equation could have more than one solution. These roots appear for particular situation depending on contamination level and type. The presence of multiple roots in the full model can create some problem in the set of weights we should use. Actually, the selection of the root is done by the minimum scale error provided. Since this choice is not always the one would choose, we introduce the min.weight parameter in order to choose only between roots that do not down weight everything. This is not still the optimal solution, and perhaps, in the new release, this part will be change.

Value

wle.stepwise returns an object of class "wle.stepwise".
The function summary is used to obtain and print a summary of the results. The generic accessor functions coefficients and residuals extract coefficients and residuals returned by wle.stepwise.
The object returned by wle.stepwise are:

wstep the iterations with the model selected.
coefficients the parameters estimator, one row vector for each root found in the full model.
scale an estimation of the error scale, one value for each root found in the full model.
residuals the unweighted residuals from the estimated model, one column vector for each root found in the full model.
tot.weights the sum of the weights divide by the number of observations, one value for each root found in the full model.
weights the weights associated to each observation, one column vector for each root found in the full model.
freq the number of starting points converging to the roots.
index position of the root used for the weights.
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.
type "Stepwise": the weighted stepwise methods is used, "Forward": the weighted forward methods is used, "Backward": the weighted backward method is used.
f.in the in value.
f.out the out value.
method if "WLS" the submodel parameters are estimated by weighted least square with weights from the weighted likelihood estimator on the full model else if "WLE" the submodel parameters are estimated by weighted likelihood estimators.

Author(s)

Claudio Agostinelli

References

Agostinelli, C., (2000) Robust stepwise regression, Working Paper n. 2000.10 del Dipartimento di Scienze Statistiche, Universit`a di Padova, Padova.

Agostinelli, C., (2000) Robust stepwise regression, submitted to Journal of Applied Statistics.

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

See Also

wle.smooth an algorithm to choose the smoothing parameter for normal distribution and normal kernel, wle.lm a function for estimating linear models with normal distribution error and normal kernel.

Examples


library(wle)

# You can find this dataset in:
# Agostinelli, C., (1999). Robust model selection in regression 
# via weighted likelihood methodology, submitted to Statistics & 
# Probability Letters.

data(selection)

result <- wle.stepwise(ydata~xdata,,boot=100,group=6,
            num.sol=3,min.weight=0.8,type="Stepwise",
            method="WLS")

summary(result)