wle (version 0.9-91)

mle.aic: Akaike Information Criterion

Description

The Akaike Information Criterion is evaluated for each submodel.

Usage

mle.aic(formula, data=list(), model=TRUE, x=FALSE,  y=FALSE, var.full=0, alpha=2, contrasts = NULL,  se=FALSE, 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 mle.aic is called from.

model, x, y

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

var.full

the value of variance to be used, if 0 the variance estimated from the full model is used.

alpha

the penalized constant.

contrasts

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

se

logical. if TRUE the returning object contains standard errors for the parameters of every model.

verbose

if TRUE warnings are printed.

Value

mle.aic returns an object of class "mle.aic".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 mle.aic. The object returned by mle.aic are:

aic

the AIC for each submodels

coefficients

the parameters estimator, one row vector for each submodel.

scale

an estimation of the error scale, one value for each submodel.

residuals

the residuals from the estimated model, one column vector for each submodel.

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.

se

standard errors of the parameters, one row vector for each submodel. Available only if se is TRUE.

Details

Models for mle.aic 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

Akaike, H., (1973) Information theory and an extension of the maximum likelihood principle, in: B.N. Petrov and F. Cs\'aki, eds., Proc. 2nd International Symposium of Information Theory, Akad\'emiai Kiad\'o, Budapest, 267-281.

Examples

library(wle)

data(hald)

cor(hald)

result <- mle.aic(y.hald~x.hald)

summary(result,num.max=10)