Clustering with latent variables

Besides continuous variables, binary indicators on ICT(Information and Communication Technologies) infrastructures andutilities are usually collected in order to evaluate the qualityof a public company and to define the policy priorities. In thispaper we face the problem of clustering public organizations byassuming that these binary attributes are generated from latentcontinuous variables and by estimating the scores of the latentvariables. In economics, these variables are called utilityfunctions and the assumption is that the binary attributes (whichmay be, for example, the presence or the absence of a publicservice or a public utility) are determined by the crossing of acertain threshold in these functions. To compare the proposedclustering approach with the latent class mixture modelling asimplemented in the Latent Gold package we simulate data from asetting where the true group membership is known. Then, we presenta cluster analysis of the Emilia-Romagna municipalities, based ona set of back office and front office indicators, thatdemonstrates the usefulness of the proposed method as a keysupport for policy makers.