The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the dimensionality of the data and improving interpretation. Because of this, we propose a modern approach to obtaining the HJ biplot called the elastic net HJ biplot, which applies the elastic net penalty to improve the interpretation of the results. It is a novel algorithm in the sense that it is the first attempt within the biplot family in which regularisation methods are used to obtain modified loadings to optimise the results. As a complement to the proposed method, and to give practical support to it, a package has been developed in the R language called SparseBiplots. This package fills a gap that exists in the context of the HJ biplot through penalized techniques since in addition to the elastic net, it also includes the ridge and lasso to obtain the HJ biplot. To complete the study, a practical comparison is made with the standard HJ biplot and the disjoint biplot, and some results common to these methods are analysed.

Quality of life, as an essential component of sustainable development, is particularly relevant in transnational contexts characterized by deep inequalities in human development, equity, and social well-being. The objective of this paper is to analyze the temporal and spatial changes in transnational patterns of quality of life observed between 2018 and 2025, taking into account levels of human development. To this end, multivariate statistical techniques were applied: partial triadic analysis, which allows the identification of both the common structure of the data and the temporal evolution of the indicators, together with the HJ-Biplot and cluster analysis, which provide a multidimensional and interpretable visualization of country profiles. The results reveal consistent configurations of quality of life, largely aligned with levels of human development, and highlight persistent inequalities in environmental quality, economic accessibility, and objective well-being. These findings are relevant for the formulation of policies aimed at enhancing population well-being, particularly in countries facing structural constraints despite their high levels of development. The contribution of this research lies in its three-dimensional, dynamic, and reproducible approach, which makes it possible to identify regional contrasts that are not visible through traditional methods based on unidimensional indicators or cross-sectional analyses.

Chlorophyll-a is a widely used indicator for assessing the trophic status and water quality of aquatic ecosystems because of its close relationship with phytoplankton biomass. This study aimed to identify the physicochemical, biological, and temporal variables associated with chlorophyll-a concentrations in Lake Gatun during the 2017–2023 period using the Light Gradient Boosting Machine (LightGBM) algorithm and a Generalized Linear Model (GLM). A total of 25 predictor variables describing water quality were analyzed using data collected from 14 monitoring stations distributed throughout Lake Gatun within the Panama Canal watershed. The LightGBM model achieved satisfactory predictive performance, with an RMSE of 4.58, an MAE of 3.26, and a coefficient of determination (R²) of 0.42 on the testing dataset. Variable importance analysis identified turbidity, dissolved oxygen, and water transparency as the most influential predictors of chlorophyll-a concentrations. These findings improve our understanding of the factors associated with chlorophyll-a variability and demonstrate the potential of machine learning models as decision-support tools for monitoring and managing aquatic ecosystems.

Food group costs constitute a fundamental component of food affordability; however, differences in their temporal evolution across food groups can make it difficult to identify common cost patterns and periods of greater differentiation within the Basic Family Food Basket. This study aimed to analyze the joint evolution and temporal structure of the costs of ten food groups included in the Basic Family Food Basket of Panama and San Miguelito over the 2018–2025 period. Monthly food-group cost data were analyzed using X-STATIS (Partial Triadic Analysis). The results showed a general upward trend in food-group costs, although different patterns of change were observed among the food groups. The interstructure revealed a clear temporal differentiation between the 2018–2021 and 2022–2025 periods, while the compromise analysis enabled the identification of the common multivariate structure underlying the study period. Likewise, the temporal trajectories showed that the food groups did not evolve homogeneously but instead exhibited different patterns of change throughout the analyzed period. In conclusion, the X-STATIS approach made it possible to simultaneously characterize the common structure and temporal dynamics of food cost, providing a multivariate perspective on the changes observed in the CBFA of Panama and San Miguelito.

Monitoring ambient air quality is essential for assessing environmental conditions and examining relationships among pollution indicators. This study presents a cross-sectional comparative analysis of key air quality indicators (PM_2.5, O₃, NO₂, SO₂, CO, and volatile organic compounds), together with a contextual variable related to pollution exposure (household solid fuels), across countries in Latin America and the Caribbean for the year 2024. The objective is to characterize air quality profiles by analyzing the interrelationships among indicators and the relative positioning of countries, integrating both elements within a multivariate framework. Multivariate statistical techniques, including HJ-Biplot and cluster analysis, were applied to provide an integrated representation of the data. The results indicate differences in the configuration of air quality indicators across countries, with some Caribbean countries associated with lower levels of pollution indicators, while several South and Central American countries are associated with higher levels. These results also suggest associations between air quality indicators and factors such as industrial activity proxies, population density, and the use of household solid fuels. Given the cross-sectional nature of the data, these findings should be interpreted as associations rather than causal relationships.