Underlying Structure in the Clustering of Peruvian Departments According to Demographic Indicators, 2022

Abstract

Territorial gaps in demographic indicators hinder the effective targeting of public policies in Peru. This study aimed to segment the 24 departments and the Constitutional Province of Callao (2022) to identify differentiated demographic profiles that support territorial planning. Following a quantitative, non-experimental, cross-sectional design, six standardized indicators were used: crude birth rate, total fertility rate, crude death rate, life expectancy at birth, infant mortality rate, and crude nuptiality rate. k-means (Lloyd, MacQueen, and Hartigan–Wong variants) and k-medoids (PAM) were applied, and cluster quality was assessed through average silhouette width, the elbow method, the gap statistic, and inter-algorithm stability (Jaccard index). Principal component analysis (PCA) supported interpretation (PC1 = 59.5 %; PC2 = 24.2 %; 83.8 % cumulative variance), and the resulting structure was contrasted with a Ward hierarchical dendrogram. The results converged on k = 2 as the main solution, given its higher silhouette (≈ 0.33), the absence of negative widths, and high replicability across algorithms; an advanced cluster (low birth and fertility rates, high life expectancy, very low infant mortality) and a lagging cluster with the opposite pattern emerged. The slightly higher crude mortality in the advanced cluster is consistent with population aging. As an operational disaggregation, k = 4 distinguished a metropolitan-southern pole, an Andean-Amazonian bloc facing greater challenges, and two intermediate transitional groups. ANOVA confirmed significant between-group differences in most indicators. The contribution is a reproducible, visualizable typology that strengthens territorial planning and the prioritization of resources for maternal-child health and basic services.