Composite indicator for ordinal data: some considerations about variable transformation and link function

Composite indicators are very important tools required in many different fields to asses, compare and rank performances, development stage, quality, and many other different targets. Typically composite indicators are devoted to measure a multi-dimensional not directly observable concept by means of a set of appropriate manifest variables (elementary indicators) which contribute to overall measure of the unobservable concept. In this paper some matters regarding methods to achieve the composite indicators are discussed assuming manifest variables are measured on ordinal categorical scale and a scaling procedure is adopted to convert observed data into numerical data. Also aggregating function and weighing system are considered and the use of dissimilarity indexes together with Kendall--association or heterogeneity indexes for weighting is suggested. An application of these techniques in satisfaction measure is then performed and compared with other alternative procedures.