Multivariate concordance measures : a proposal

We propose a novel multivariate measure of goodness of fit for a multiple linear regression model when the relevant involved explanatory variables assume mostly categorical nature. The proposed measure is based on the response variable Lorenz curve and its dual construction. Once the linear regression estimates are obtained, one can proceed by defining the concordance curve represented by the response variable original values ordered according to the ranks assigned to the corresponding estimated values. The concordance curve position explains the goodness of fit of the multiple linear regression model to the data. We also provide an extension of the Lorenz curve definition for ordinal variables in order to develop a further concordance index in this case.