Exploring competitiveness and wellbeing in Italy by spatial principal component analysis

Well being is a multidimensional phenomenon, that cannot be measured by a single descriptive indicator and that, it should be represented by multiple dimensions. It requires, to be measured by combination of different dimensions that can be considered together as components of the phenomenon. This combination can be obtained by applying methodologies knows as Composite Indicators (CIs). CIs are largely used to have a comprehensive view on a phenomenon that cannot be captured by a single indicator. Principal Component Analysis (PCA) is one of the most popular multivariate statistical technique used for reducing data with many dimension, and often well being indicators are obtained using PCA. PCA is implicitly based on a reflective measurement model that it non suitable for all types of indicators. Mazziotta and Pareto (2013) in their paper discuss the use and misuse of PCA for measuring well-being. The classical PCA is not suitable for data collected on the territory because it does not take into account the spatial autocorrelation present in the data. The aim of this paper is to propose the use of Spatial Principal Component Analysis for measuring well being in the Italian Provinces.

An Eigenvalue Test for spatial Principal Component Analysis

BackgroundThe spatial Principal Component Analysis (sPCA, Jombart 2008) is designed to investigate non-random spatial distributions of genetic variation. Unfortunately, the associated tests used for assessing the existence of spatial patterns (global and local test; Jombart et al. 2008) lack statistical power and may fail to reveal existing spatial patterns. Here, we present a non-parametric test for the significance of specific patterns recovered by sPCA.ResultsWe compared the performance of this new test to the original global and local tests using datasets simulated under classical population genetic models. Results show that our test outperforms the original global and local tests, exhibiting improved statistical power while retaining similar, and reliable type I errors. Moreover, by allowing to test various sets of axes, it can be used to guide the selection of retained sPCA components.ConclusionsAs such, our test represents a valuable complement to the original analysis, and should prove useful for the investigation of spatial genetic patterns.