A Probabilistic Model for the Distribution of GDP per Capita in NUTS 3 Zones of Europe

A macroeconomic indicator of productivity and economic development, used to obtain information on the economic and social conditions of a country, is the GDP per capita, which is also used as an indicator of social welfare. By construction it can be used directly to compare areas of interest. It is an indicator of great variability to which it is difficult to assign a probabilistic model to describe its distribution. In fact, it usually appears as a strongly asymmetric and frequently multimodal variable, which directly indicates a strong non-normality. In this work we propose to deal with the problem of finding a probabilistic model for this variable through the estimation of a model of finite mixtures of normal distributions. As an application example, we present the model obtained through the finite mixture for GDP per capita data from the NUTS 3 zones in the nomenclature of the European Union, EU countries and neighbouring countries. Thus, the model is estimated, its validity is checked and the results obtained are analysed, both for the GDP per capita variable and as a function of the countries to which the studied areas belong.

Finite Mixture Modeling for Program Evaluation: Resampling and Pre-processing Approaches

Background Finite mixture models cluster individuals into latent subgroups based on observed traits. However, inaccurate enumeration of clusters can have lasting implications on policy decisions and allocations of resources. Applied and methodological researchers accept no obvious best model fit statistic, and different measures could suggest different numbers of latent clusters. Objectives The purpose of this article is to evaluate and compare different cluster enumeration techniques. Research Design Study I demonstrates how recently proposed resampling methods result in no precise number of clusters on which all fit statistics agree. We recommend the pre-processing method in Study II as an alternative. Both studies used nationally representative data on working memory, cognitive flexibility, and inhibitory control. Conclusions The data plus priors method shows promise to address inconsistencies among fit measures and help applied researchers using finite mixture models in the future.

Characterizing Stand and Biomass Tables from Diameter Distribution Models: A Case Study for Mixed-Hardwood Forests in Eastern Tennessee, USA

Accurately assessing forest structure and productivity is critical to making timely management decisions and monitoring plant communities. This study aims to evaluate the prediction accuracy of site-level stand and biomass tables from the diameter distribution models. The efficacy of the single Weibull function and two finite mixture models was compared for six species groups on three mixed-hardwood sites in eastern Tennessee, USA. To evaluate model performance, two types of stand/biomass tables were generated. The first type was constructed from all species on a given site (site-specific), whereas the second type was built for a single species from all sites (species-specific). Results indicate that both types of stand and biomass tables were consistently well quantified by the two-component mixture model in terms of goodness of fit, parsimony and robustness. The two-component mixture model better characterized the complex, multimodal diameter distributions than the single Weibull model, which underpredicted the upper portion of the distributions. The three-component model tends to overfit the data, which results in lower prediction accuracy. Among the three models examined, the two-Weibull mixture model is suggested to construct site-level stand/biomass tables, which provides more reliable and accurate predictions to assess forest structure and product class. Study Implications Compared to pine monocultures, diameter distribution models for upland mixed-hardwood forests in the Southeastern United States have not been widely explored. Mixed-hardwood forests not only supply high-quality timber for domestic and international uses, but also provide various ecosystem services and essential habitats for wildlife. The finite mixture model has been proposed for characterizing the irregular forms of diameter distribution curves, but the reliability of this method has not been explicitly examined for a wide variety of species. This study provided insights for natural resources managers to select appropriate models when modeling stand and biomass tables for mixed-hardwood forests.