VUROCS-package {VUROCS}

Volume under the ROC Surface for Multi-Class ROC Analysis

Description

Calculates the volume under the ROC surface and its (co)variance for ordered multi-class ROC analysis as well as certain bivariate ordinal measures of association.

Details

The package VUROCS provides three core functions to determine the volume under the ROC surface (VUS) as well as the variance and covariance of the VUS. The implementation is generally based on the algorithms presented in Waegeman, De Baets and Boullart (2008).

• VUS(y,fx) calculates the VUS for a vector of realizations y and a vector of predictions fx.

• VUSvar(y,fx) calculates the variance of VUS for a vector of realizations y and a vector of predictions fx.

• VUScov(y,fx1,fx2) calculates the covariance of the two VUS implied by the predictions fx1 and fx2 for a vector of realizations y.

In addition to these three core functions, the package also provides an implementation of the cumulative LGD accuracy ratio (CLAR) suggested by Ozdemir and Miu (2009) specially for the purpose of assessing the discriminatory power of Loss Given Default (LGD) credit risk models. The CLAR as well as an adjusted version are computed by the functions clar and clarAdj. Moreover, the package provides time-efficient implementations of Somers' D , Kruskall's Gamma, Kendall's Tau_b and Kendall's Tau_c in the functions SomersD, Kruskal_Gamma, Kendall_taub and Kendall_tauc. These functions also compute asymptotic standard errors defined by Brown and Benedetti (1977) and Goktas and Oznur (2011).

Author(s)

Kazianka Hannes, Morgenbesser Anna, Nowak Thomas

References

Brown, M.B., Benedetti, J.K., 1977. Sampling Behavior of Tests for Correlation in Two-Way Contingency Tables. Journal of the American Statistical Association 72(358), 309-315

Goktas, A., Oznur, I., 2011. A Comparison of the Most Commonly Used Measures of Association for Doubly Ordered Square Contingency Tables via Simulation. Metodoloski zvezki 8 (1), 17-37

Ozdemir, B., Miu, P., 2009. Basel II Implementation: A Guide to Developing and Validating a Compliant, Internal Risk Rating System. McGraw-Hill, USA.

Waegeman W., De Baets B., Boullart L., 2008. On the scalability of ordered multi-class ROC analysis. Computational Statistics & Data Analysis 52, 3371-3388.

Examples

y  <- rep(1:5,each=3)
fx <- c(3,3,3,rep(2:5,each=3))

VUS(y,fx)
clar(y,fx)
clarAdj(y,fx)
SomersD(y,fx)
Kruskal_Gamma(y,fx)
Kendall_taub(y,fx)
Kendall_tauc(y,fx)

VUSvar(rep(1:5,each=3),c(1,2,3,rep(2:5,each=3)))
VUScov(c(1,2,1,3,2,3),c(1,2,3,4,5,6),c(1,3,2,4,6,5))