# Estimate CAR Scores and Marginal Correlations

### Description

`carscore`

estimates the vector of CAR scores, either using the standard
empirical estimator of the correlation matrix, or a shrinkage estimator.

### Usage

1 |

### Arguments

`Xtrain` |
Matrix of predictors (columns correspond to variables). |

`Ytrain` |
Univariate response variable. |

`lambda` |
The correlation shrinkage intensity (range 0-1).
If not specified (the default) it is estimated using an
analytic formula from Sch\"afer and Strimmer (2005). For |

`diagonal` |
For |

`verbose` |
If |

### Details

The CAR scores are the correlations between the response and the Mahalanobis-decorrelated predictors. CAR score is an abbreviation for Correlation-Adjusted (marginal) coRelation, where the first correlation matrix refers dependencies among predictors.

In Zuber and Strimmer (2011) it is argued that squared CAR scores are a natural measure for variable importance and it is shown that variable selection based on CAR scores is highly efficient compared to competing approaches such as elastic net lasso, or boosting.

If the response is binary (or descrete) the corresponding quantity
are CAT scores (see `catscore`

).

### Value

`carscore`

returns
a vector containing the CAR scores (or marginal correlations for `diagonal=TRUE`

).

### Author(s)

Verena Zuber and Korbinian Strimmer (http://strimmerlab.org).

### References

Zuber, V., and K. Strimmer. 2011. High-dimensional regression and variable selection using CAR scores. Statist. Appl. Genet. Mol. Biol. 10: 34. http://www.bepress.com/sagmb/vol10/iss1/art34/

### See Also

`catscore`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | ```
# load care library
library("care")
######
# empirical CAR scores for diabetes data
data(efron2004)
xnames = colnames(efron2004$x)
n = dim(efron2004$x)[1]
car = carscore(efron2004$x, efron2004$y, lambda=0)
car
# compare orderings
# variables ordered by squared CAR scores
xnames[order(car^2, decreasing=TRUE)]
# "bmi" "s5" "bp" "s3" "s4" "s6" "sex" "age" "s2" "s1"
# compare with ordering by t-scores / partial correlations
pcor = pcor.shrink(cbind(efron2004$y,efron2004$x), lambda=0, verbose=FALSE)[-1,1]
xnames[order(pcor^2, decreasing=TRUE)]
# "bmi" "bp" "s5" "sex" "s1" "s2" "s4" "s6" "s3" "age"
# compare with ordering by marginal correlations
mcor = cor(efron2004$y,efron2004$x)
#mcor = carscore(efron2004$x, efron2004$y, diagonal=TRUE, lambda=0)
xnames[order(mcor^2, decreasing=TRUE)]
# "bmi" "s5" "bp" "s4" "s3" "s6" "s1" "age" "s2" "sex"
# decomposition of R^2
sum(car^2)
slm(efron2004$x, efron2004$y, lambda=0, lambda.var=0)$R2
# pvalues for empirical CAR scores
pval = 1-pbeta(car^2, shape1=1/2, shape2=(n-2)/2)
pval <= 0.05
######
# shrinkage CAR scores for Lu et al. (2004) data
data(lu2004)
dim(lu2004$x) # 30 403
# compute shrinkage car scores
car = carscore(lu2004$x, lu2004$y)
# most important genes
order(car^2, decreasing=TRUE)[1:10]
# compare with empirical marginal correlations
mcor = cor(lu2004$y, lu2004$x)
order(mcor^2, decreasing=TRUE)[1:10]
# decomposition of R^2
sum(car^2)
slm(lu2004$x, lu2004$y)$R2
``` |