ADVICE (version 1.0)

ices: Interrupted Coefficient Estimation Selection

Description

This function provides an alternative multiple regression fitting procedure which simultaneously estimates and selects variables. The resulting coefficient estimates will tend to be slightly biased, but in a sparse setting, they can be quite accurate. A full regression model is specified by the user, and the function usually returns coefficient estimates for a reduced model, i.e., a model for which some of the coefficient estimates are exactly 0.

Usage

ices(formula, data, model = TRUE, x = FALSE, y = FALSE, qr = TRUE)

Arguments

formula

a formula object specifying the full regression model.

data

a data frame containing observations on the response variable and the predictor variables.

model, x, y, qr

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

Value

a QRS class object

coefficients

a named numeric vector of coefficients

residuals

a numeric vector containing the response minus the fitted values.

effects

a numeric vector of containing the projections of the response variable under the orthogonal Q matrix coming from the QR decomposition of the model matrix.

rank

the numeric rank of the fitted linear model.

fitted.values

the estimated response values according to the fitted interrupted coefficient estimation selection regression model.

sigma2

the estimated noise variance based on the n-p residual effects, where p is the size of the full model.

std_error

a numeric vector of standard errors.

df.residual

residual degrees of freedom.

x

a numeric matrix containing the model matrix.

y

a numeric vector containing the response variable values.

qr

the QR decomposition object coming from the model matrix (after re-ordering columns).

coefOrder

permutation of the sequence 1:p which gives the ascending order of the coefficients of the linear model object, as a result of the pre-screening.

call

the matched call.

terms

the terms object used.

names

a character vector containing the column names of the model matrix.

model

if requested (the default), the model frame used in the case of the full regression model.

See Also

lm.R, QRS.R

Examples

# NOT RUN {
    myRegressionData <- rmultreg(50, k=10, p=.25, sdnoise = .5)
    pairs(myRegressionData$data)
    out <- ices(y ~ ., data = myRegressionData$data) # fit model to simulated data
    confint(out) # calculate 95 % confidence intervals for all coefficients
    myRegressionData$coefficients # compare with true coefficients
# }