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The wavelet-based confirmatory factor analysis of longitudinal data as a new approach to studying dynamical characteristics of complex systems


L.S. Kuravsky, P.A. Marmalyuk, S.N. Baranov, V.I. Abramochkina, E.A. Petrova

A new technology for revealing and studying factors responsible for evolution of complex systems is under consideration. It combines capabilities of wavelet transforms and identified factor structures. According to the proposed approach, the samples of coefficients resulted from discrete wavelet transform of initial parameter time series under study and responsible for different observation periods are considered as values of observed variables in the subsequent confirmatory factor analysis to reveal time history of factor influences and estimates of factor interaction. Identification of free factor model parameters (usually factor variances and covariances) is carried out by a new direct (noniterative) procedure based on the maximum likelihood method, which is an alternative to traditional local iterative solution of optimization problems. A statistical method to check significance of factor model components is discussed. Presented are advantages of the given approach over the traditional simplex method as well as a set of approaches to development of factor models represented by path diagrams including their comparison.

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