Classification of local labor markets in the Wielkopolskie voivodship in the light of principal component analysis for doubly multivariate data

Wojciech Łukaszonek; Marcin Szymkowiak; Waldemar Wołyński

doi:https://doi.org/10.59139/stattrans-2026-026

Classification of local labor markets in the Wielkopolskie voivodship in the light of principal component analysis for doubly multivariate data

Wojciech Łukaszonek 1Interfaculty Institute of Mathematics and Statistics, Calisia University & Statistical Office in Pozna´n, Pozna´n, Poland ORCID:https://orcid.org/0000-0001-8109-2901 , Marcin Szymkowiak Institute of Informatics and Quantitative Economics, Poznań University of Economics and Business, Poznań, Poland & Statistical Office in Poznań, Poznań, Poland ORCID:https://orcid.org/0000-0003-3432-4364 , Waldemar Wołyński Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland ORCID:https://orcid.org/0000-0002-0777-9163 Statistics in Transition new series, vol. 27, 2026, 3, pages: 25-46 Published online: 9 September 2026 https://doi.org/10.59139/stattrans-2026-026 Citation: Łukaszonek W., Szymkowiak M., Wołyński W., 2026. Classification of local labor markets in Wielkopolskie province in light of principal component analysis for doubly multivariate data. Statistics in Transition new series, 27(3), pp. 25-46. https://doi.org/10.59139/stattrans-2026-026

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ABSTRACT

The main aim of this article is to evaluate the situation in the local labor markets of the Wielkopolskie voivodship at the county level using principal component analysis for doubly multivariate data, in three variants: classical principal component analysis (PCA), a kernel model (KPCA) and a functional data model (FPCA). This will be done using doubly multivariate data, i.e. data that are characterized by both the variability of features and the variability over time. Since the use of classical PCA for doubly multivariate data raises some problems related to the appropriate estimation of the covariance matrix, the authors propose the use of a non-linear kernel model and a model for functional data to overcome this inconvenience.
The analysis of local labor markets in the Wielkopolskie voivodship based on 12 observed variables between 2004 and 2022 showed that similar clustering results were achieved for all the considered approaches. However, a substantial increase in the explained variance was only achieved in relation to PCA in the case of FPCA. Equally important is that unlike classical PCA, which treats each time point as a separate variable, FPCA models the entire time trajectory as a functional object. This preserves the temporal continuity and allows the capture of important dynamics such as trends, seasonal patterns, and structural breaks that characterize labor markets.
The methodology proposed in this article is flexible and can be successfully used in other research areas including poverty, socio-economic development or disability, particularly where both feature variability and temporal dynamics play important roles in understanding complex socioeconomic phenomena.

KEYWORDS

local labor markets, doubly multivariate data, principal component analysis, functional principal component analysis, kernel principal component analysis, cluster analysis

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