care (version 1.0.0)

fitlm: Estimation of Regression Coefficients

Description

fitlm fits regression coefficients by plugin of shrinkage or empirical estimates of correlations and variances.

Usage

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

Arguments

x

matrix of predictors (columns correspond to variables).

y

univariate response variable.

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

• fitlm returns a list with the estimated partial correlations, the regression coefficients, and the intercept.

Details

The regression coefficients are fitted by estimating the joint covariance matrix of the response and the predictors, which is then inverted and used for computing regression coefficients - see Opgen-Rhein and Strimmer (2007). As estimators for the covariance matrix either the standard empirical estimator or a Stein-type shrinkage estimator is employed. The use of the empirical covariance leads to the OLS estimates of the regression coefficients, whereas otherwise shrinkage estimates are obtained. The function also returns the partial partial correlations between each predictor and the response. These provide the standard ordering of variables (identical to the ordering of p-values or t-scores computed by lm, see example below) but different from the ranking provided by CAR scores (cf. carscore).

References

Opgen-Rhein, R., and K. Strimmer. 2007. From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst. Biol. 1: 37. (http://www.biomedcentral.com/1752-0509/1/37/abstract)

See Also

carscore

Examples

# load care library
library("care")

# diabetes data
data(efron2004)
x = efron2004$x
y = efron2004$y
n = dim(x)[1]
p = dim(x)[2]

# empirical regression coefficients
fit = fitlm(x, y, estimator="empirical")
fit

# t scores corresponding to partial correlations
df = n-p-1
r = fit$pcor
t = r * sqrt(df/(1-r^2))
t.pval = 2 - 2 * pt(abs(t), df)

cbind(fit$b, t, t.pval)

# compare results with lm
summary(lm(y ~ x))