Aplicación de Métodos Variacionales para la Inferencia Estadística Bayesiana : Inferencia Variacional para la estimación de parámetros enn modelos de Teoría de Respuesta al Ítem.

Abstract

Item Response Theory (IRT) attempts to measure latent traits through statistical models. In recent years, many applications have been made for evaluating academic performance, measuring skills, competences, etc. (Matas A., 2010). The present work attempts to measure the political interest of a group of individuals using the answers provided in survey. There are a variety of models that allow to estimate the probability of answering a question correctly, given the ability, difficulty and/or pseudo-random parameters for each item, as the case may be. More details about these models are shown in (Hambleton R. K., Van der Linden W. J., 1997).

When estimating the distribution of the latent variable, it is quite common to use Maximum Likelihood, Monte Carlo via Markov Chains methods, among others. There is another way to estimate this probability, which is used in the present work, that is Variational Inference; this method approximates densities of probability by optimization. The idea is to transform the initial problem to another where our new goal is to choose the member of a distribution family that best approximates the posterior density of the latent variable, the political interest in this case, minimizing an estimate of the distance between true and approximate distributions. For this, the Kullback-Leibler divergence is used (Wu M., Davis R.L., Domingue B. W., Piech C., & Goodman, N., 2020).