Principal component analysis approaches for doubly multivariate functional data of local labour markets in wielkopolskie
摘要
This study investigates the structure and dynamics of local labour markets in the Wielkopolskie province (Poland) using a doubly multivariate framework that simultaneously captures cross-sectional heterogeneity and temporal evolution. Classical principal component analysis (PCA) faces well-known limitations in this setting, particularly due to high dimensionality, multicollinearity, and the instability of covariance estimation when the number of observations is small relative to the data dimension. To address these challenges, we propose a comparative framework combining kernel principal component analysis (KPCA) and functional principal component analysis (FPCA). While KPCA introduces non-linearity through kernel mappings, FPCA models each variable as a continuous function over time, thereby preserving temporal dependence and structural dynamics. Using a dataset of 35 counties observed over the period 2004–2022 and described by 12 labour market indicators, we show that FPCA substantially improves the proportion of explained variance compared to both PCA and KPCA. Despite these differences, all approaches yield highly consistent clustering structures, revealing robust spatial patterns characterized by a strong core–periphery gradient centered around Poznaǹ. Beyond methodological contributions, we provide a critical discussion on the trade-off between dimensionality reduction, interpretability, and representation capacity in composite indicator construction. The proposed framework offers a flexible and scalable approach for analyzing complex socio-economic systems with multi-dimensional and temporal dependencies. The findings highlight a trade-off between interpretability and informational richness, and demonstrate that modelling temporal continuity is more critical than capturing non-linearity in this context. The proposed framework contributes to the literature on composite indicators and provides a flexible tool for regional policy analysis in multidimensional and dynamic settings.