Variable Weighting via Multidimensional IRT Models in Composite Indicators Construction

One of the most controversial steps in Composite Indicators (CIs) construction is the selection of one (possibly) best weighting technique. In this paper, we introduce a new endogenous weighting methodology developed in an extended Item Response Theory (IRT) framework. As weighting is much more thorough when carried out by accounting for the dimensionality of a dataset rather than by ignoring it, we suggest to assign weights on the basis of the discriminant parameters estimated through a multidimensional two-parameter logistic IRT model. Specifically, the procedure is developed through two consecutive steps. The first applies a hierarchical clustering algorithm to ascertain the number of dimensions measured by the data. The second estimates the discriminating parameters under the multidimensional two-parameter logistic model selected at the first step. The discriminating parameters can then be used to compare and weight the items that refer to the same dimension. Be- sides, in order to make such discriminating indices comparable across dimensions, the distribution of the latent trait is standardised for each dimension. The potentialities of this novel weighting technique are illustrated through an application to educational data, which refer to a national standardised test developed and collected by the Italian National Institute for the Evaluation of the Education System (INVALSI).