catscore {sda}

Estimate CAT Scores and t-Scores

Description

catscore computes CAT scores (correlation-adjusted t-scores) between the group centroids and the pooled mean.

Usage

catscore(Xtrain, L, lambda, lambda.var, lambda.freqs, diagonal=FALSE, verbose=TRUE)

Arguments

Xtrain

A matrix containing the training data set. Note that the rows correspond to observations and the columns to variables.

L

A factor with the class labels of the training samples.

lambda

Shrinkage intensity for the correlation matrix. If not specified it is estimated from the data. lambda=0 implies no shrinkage and lambda=1 complete shrinkage.

lambda.var

Shrinkage intensity for the variances. If not specified it is estimated from the data. lambda.var=0 implies no shrinkage and lambda.var=1 complete shrinkage.

lambda.freqs

Shrinkage intensity for the frequencies. If not specified it is estimated from the data. lambda.freqs=0 implies no shrinkage (i.e. empirical frequencies) and lambda.freqs=1 complete shrinkage (i.e. uniform frequencies).

diagonal

for diagonal=FALSE (the default) CAT scores are computed; otherwise with diagonal=TRUE t-scores.

verbose

Print out some info while computing.

Details

CAT scores generalize conventional t-scores to account for correlation among predictors (Zuber and Strimmer 2009). If there is no correlation then CAR scores reduce to t-scores. The squared CAR scores provide a decomposition of Hotelling's T^2 statistic.

CAT scores for two classes are described in Zuber and Strimmer (2009), for the multi-class case see Ahdesm\"aki and Strimmer (2010).

The scale factors for t-scores and CAT-scores are computed from the estimated frequencies (for empirical scale factors set lambda.freqs=0).

Value

catscore returns a matrix containing the cat score (or t-score) between each group centroid and the pooled mean for each feature.

Author(s)

Verena Zuber, Miika Ahdesm\"aki and Korbinian Strimmer (https://strimmerlab.github.io).

References

Ahdesm\"aki, A., and K. Strimmer. 2010. Feature selection in omics prediction problems using cat scores and false non-discovery rate control. Ann. Appl. Stat. 4: 503-519. <DOI:10.1214/09-AOAS277>

Zuber, V., and K. Strimmer. 2009. Gene ranking and biomarker discovery under correlation. Bioinformatics 25: 2700-2707. <DOI:10.1093/bioinformatics/btp460>

See Also

sda.ranking, carscore,.

Examples

# load sda library
library("sda")

################# 
# training data #
#################

# prostate cancer set
data(singh2002)

# training data
Xtrain = singh2002$x
Ytrain = singh2002$y
dim(Xtrain)


####################################################
# shrinkage t-score (DDA setting - no correlation) #
####################################################

tstat = catscore(Xtrain, Ytrain, diagonal=TRUE)
dim(tstat)
tstat[1:10,]


########################################################
# shrinkage CAT score (LDA setting - with correlation) #
########################################################

cat = catscore(Xtrain, Ytrain, diagonal=FALSE)
dim(cat)
cat[1:10,]