On the construction of an aggregated measure of the development of interval data

We analyse some possibilities for constructing an aggregated measure of the development of socio-economical objects in terms of their composite phenomenon (i.e., phenomenon described by many statistical features) if the relevant data are expressed as intervals. Such a measure, based on the deviation of the data structure for a given object from the benchmark of development is a useful tool for ordering, comparing and clustering objects. We present the construction of a composite phenomenon when it is described by interval data and discuss various aspects of stimulation and normalization of the diagnostic features as well as a definition of a benchmark of development (based usually on optimum or expected levels of these features). Our investigation includes the following options for the realization of this purpose: transformation of the interval model into a single–valued version without any significant loss of its statistical properties, standardization of pure intervals as well as definition of the interval “ideal” object. For the determination of a distance between intervals, the Hausdorff formula is applied. The simulation study conducted and the empirical analysis showed that the first two variants are especially useful in practice. Copyright Springer-Verlag Berlin Heidelberg 2014