The Quality-of-Life Measurement with a Stochastic Choice of Parameters of the Weighted Principal Component

Abstract

The quality of life of the population is a latent category, and due to the impossibility of direct measurement it has to be assessed as an integral indicator of many variables. According to the established methodology, one of the main tools in this case is the first principal component, that is, a linear convolution of variables, which has the property of minimizing the variation of the original characteristics. The fact that parameters’ variation is taken into account with equal weight may cause criticism from economists. The use of a weighted principal component which is free of this drawback can be considered as a development of the initial method. In this case to minimize the total variation, the weighting coefficients of features are set expertly. However, in this case, a logical question arises: won’t expert subjectivity have a significant impact on the final integral indicator, as it happens in the case of simple linear convolution with expert weights? Thus, the purpose of this work is to test the applicability of the weighted first principal component as the main tool in constructing an integral indicator of the population quality of life. In particular, it is necessary to test the hypothesis that the influence of heterogeneity in the weights of expert assessments on the final integral indicator is insignificant. In this case, it would be useful not only to illustrate the presence or absence of this influence, but also to estimate its extent. To do this, the simulation modeling is carried out to assess the latent variable “quality of life of the population”, based on empirical expert weights and macro statistics data. Moreover, in contrast to most works related to the topic, the values of the integral indicator (and, accordingly, the ranking of observations) are presented as an interval estimate. In other words, the result is presented as a random variable where the element of randomness is the subjectivity of the expert choice of weights for the weighted principal component. It turns out that even in this case it is possible to obtain robust and meaningful results that are in good agreement with the conclusions of well-known research in this area.