Estimación del Rendimiento Medio en las Pruebas PISA 2018. Un Enfoque Espacial Desde la Estimación en Áreas Pequeñas

Abstract

Estimating students' abilities in PISA tests is done using plausible values obtained through a three-parameter logistic model. With this methodology, only the information captured in the tests is taken into account, and estimates can only be made for countries and economies belonging to the OECD (domains) that were sampled. To improve the precision of the estimates and be able to make estimates in unsampled domains that have available and reliable auxiliary information, Tellez (2020) proposed using the small area estimation methodology through a Fay-Herriot model. This methodology incorporates external auxiliary information captured in addition to the test and allows for more precise estimates.

In this research, the methodology proposed by Tellez (2020) is extended by including spatial variability in the small area estimation technique. This is achieved by using the spatial Fay-Herriot model, which takes into account the spatial autocorrelation among domains. This approach is specifically applied to the reading and mathematics tests of PISA 2018. The auxiliary information used in the spatial Fay-Herriot model includes variables associated with education, science, technology, sociodemographic characteristics, economy, infrastructure, and development. These auxiliary variables provide additional information to improve the precision of the estimates of students' abilities in the domains.