care (version 1.0.0)

care: Compute CAR Regression Models

Description

care estimates CAR regression models, i.e. it first computes the CAR scores. Subsequently, the variables are included in the model in the order given by the squared CAR scores. See Zuber and Strimmer (2010) for details.

Usage

care(x, y, numpred, estimator=c("empirical", "shrinkage"), verbose=TRUE)

Arguments

x

matrix of predictors (columns correspond to variables).

y

univariate response variable.

numpred

number of included predictors (may be a scalar or a vector).

estimator

either "empirical" (the default) or "shrinkage".

verbose

if verbose=TRUE then the shrinkage intensity used in estimating the shrinkage correlation matrix is reported.

Value

• care returns a matrix of regression coefficients.

Details

The CAR scores are the correlations between the response and the Mahalanobis-decorrelated predictors. In Zuber and Strimmer (2010) it is argued that squared CAR scores are a natural measure for variable importance --- see http://arxiv.org/abs/1007.5516 for details.

References

Zuber, V., and K. Strimmer. 2010. Variable importance and model selection by decorrelation. http://arxiv.org/abs/1007.5516.

See Also

carscore, fitlm.

Examples

library("care")

# diabetes data
data(efron2004)
x = efron2004$x
y = efron2004$y
xnames = colnames(x)

#####

# ordering of the variables using squared CAR score
car = carscore(x, y)
xnames[order(car^2, decreasing=TRUE)]

# CAR regression models with 5, 7, 9 included predictors
care(x, y, numpred=c(5,7,9))

#####

# plot regression coefficients for all possible CAR models
p = 10
bmat= care(x, y, 1:p)[,-1]
bmat

plot(1:p, bmat[,1], type="l", 
  ylab="estimated regression coefficients", 
  xlab="number of included predictors", 
  main="CAR Regression Models for Diabetes Data", 
  xlim=c(1,p+1), ylim=c(min(bmat), max(bmat)))

for (i in 2:p) lines(1:p, bmat[,i], col=i, lty=i)
for (i in 1:p) points(1:p, bmat[,i], col=i)
for (i in 1:p) text(p+0.5, bmat[p,i], xnames[i])