Cluster-wise modelling: some issues considered through the example of migrations at municipality level in Poland

Abstract An experiment is presented of cluster-wise modelling, related to modelling and analysis of internal migration flows in Poland at the municipality level (some 2500 units). The experiment was carried out within a project, in which it was assumed that migration flows linearly depend upon unemployment. This simple dependence was positively verified, and the associated model error maps, corresponding to the consecutive years over two decades (2003-2022) provide a very clear and telling spatial image. Yet, the models obtained were statistically rather feeble. So, it was decided to experiment, in particular, with a set of analogous models, identified for subsets (clusters) of municipalities, employing a simile of classical k-means clustering procedure. Given the known dependence of the outcome from the k-means-like procedure upon the starting point, various initial configurations were considered. The results are exemplified in this paper, the problems appearing indicated, and some broader conclusions are drawn therefrom.