Multivariate range modeling, a new technique for multivariate class modeling: the uncertainty of the estimates of sensitivity and specificity

MRM, multivariate range modeling, is based on models built as parallelepipeds in the space of the original variables and/or of discriminant variables as those of linear discriminant analysis. The ranges of these variables define the boundary of the model. The ranges are increased by a "tolerance" factor to take into account the uncertainty of their estimate. MRM is compared with UNEQ (the modeling technique based on the hypothesis of multivariate normal distribution) and with SIMCA (based on principal components) by means of the sensitivities and specificities of the models, the estimates of type I (sensitivity) and II error rates (specificity) evaluated both with the final model built with all the available objects and by means of cross validation. UNEQ and SIMCA models were obtained with the usual critical significance value of 5% and with the model forced to accept all the objects of the modeled category. The performance parameters of the class models are critically discussed focusing on their uncertainty.