Variable analysis by means of ROC curves and categorical models.

Formal relationship between the relative (or receiver) operating characteri stics (ROC) models and the analytical models for categorical data is propos ed. Traditionally, some differences have been established between signal de tection theory (TDS) models and Generalized Linear Models (GLMs). However, some authors have suggested some specific relations (v.g. Dorfman y Alf, 19 68; Swets, 1986; DeCarlo, 1998 and Tosteson y Begg, 1988). For example, the categorical models generate results in a contingence table similar to the conditional responses to TDS. Therefore, it is possible to include standard measures of association derived from statistical models (Bishop Fienberg a nd Holland, 1975).Hence, same measures are function of the cross-product ra tio (independent of marginal totals) as LOR, eta and Q. These indices are a lso consistent with a variable-criterion model (Swets, 1986, 1996), and ROC analysis can by applied. There are also other indices consistent whith ROC analysis that imply a threshold model. In short, we propound that it is po ssible to evaluate the empirical data by using two models that can be compl ementary: TDS and GLMs models.