Analysis of indicators of the moral state of society in Europe: assessment of the adequacy of the factor model using criterion based on the self-organizing map (Kohonen map) ¹²⁰⁹

The proper use of the maximum likelihood method for the identification of the free parameters values and assessment of the factor model adequacy level in the confirmatory factor analysis of the wavelet transformations results suggests verification of the multivariate normality of observed variables. But this procedure is laborious and often impossible when a sample is small. In order to overcome this problem a new statistical criterion is proposed for the assessment of the adequacy level of factor models of dispersion components within the limits of the sample used in the study. This criterion is based on the affordances of Kohonen self-organizing maps and allows to remove constraints from the results of observation, related to their probability distribution. Advantages of the proposed criteria: – no need to test the multivariate normal distribution of observed variables; – a simple procedure for estimating the statistical errors of the second kind is available; – it is possible to estimate the most likely percent of statistically significant deviations of the components of the vector of error of the misalignment of false solutions. The article presents the theoretical basis for the development of the proposed criterion, as well as the results of its applying in the study of the common factor and the assessment of its influence on the variability of socio-economic indicators of the European countries.

Keywords: longitudinal studies, monitoring, confirmatory factor analysis, wavelet transformation, model adequacy, Kohonen self-organizing maps

Column: Mathematical Psychology