Aplicación del Algoritmo de Expectación-Maximización con Bootstrap para la Imputación de Indicadores en Modelos de Regresión Beta Multinivel Bayesianos con Enlace Logit: Un Análisis de Panel para Explicar la Relación del Gasto Público en Educación, el Factor Productivo Nacional y el Factor Demográfico sobre la Pobreza en Educación del 2015 al 2023

Abstract

In 2015, the United Nations (UN) established 17 Sustainable Development Goals (SDGs), with the primary aim of eradicating poverty, ensuring prosperity, and protecting the environment. These goals have a follow-up and evaluation agenda until 2030. Using official national data, historical variables were identified related to education poverty indicators, public spending on education, demographic factors (population density and migration), and per capita gross domestic product (GDP) at the departmental level.

To analyze education poverty data at the departmental level between 2015 and 2018, the Expectation-Maximization with Bootstrap algorithm was applied, improving the robustness of the model due to the lack of historical data. Subsequently, a Multilevel Beta Regression model with logit link was used to assess the relationship between education poverty and variables such as public spending, demographic factors, and economic production at the departmental level from 2015 to 2023.

The results showed no significant relationship between population density and education poverty, while the relationship between public spending and education poverty proved to be significant and relevant. Furthermore, national economic production had a positive and important relationship with education poverty indicators. The study also highlighted inequality in access to education in peripheral departments of the country. Although public spending is higher in areas with worse indicators, the focus and control of resources still need improvement. Finally, it was demonstrated that the imputation through the EMB algorithm better captured trends and relevant information about the educational context in Colombia.