Seleção de modelos de associação RC utilizando reversible jump MCMC - Ferreira, Flávio Fagundes (Universidade Federal de São Carlos, 2025)
The RC (Rows and Columns) association model of order K applied in contingency table analysis provides the values of the parameter estimates that evaluate the degree of association between the categories of the variables arranged in rows and columns of the table. We propose a new methodology for estimating the order K of the association model using Bayesian inference and reversible jump by MCMC (RJMCMC). In the graphics, we illustrated the groupings through credible intervals to confirm the results obtained by RJMCMC. We applied the proposed methodology to simulated data to validate the method and also to data from previous studies for comparison purposes, and the results were convergent. We subsequently we applied the proposed methodology to three real databases to assess the performance of Enem 2023 participants in the language, mathematics and writing tests according to their father’s and mother’s education. We conclude that there is an association between some categories performance and education. There is a graphical indication of grouping of rows and columns both in the results with simulated data and in the results of the comparative study.
Model selection for the RC association model using reversible jump MCMC
Keywords: Modelo de associação RC; Tabela de contingência; Inferência Bayesiana; Procrustes; Biplot; Metroplis-Hastings; Reversible Jump MCMC; RC association models; Contingency table; Bayesian inference; Procrustes; Biplot; Metroplis-Hastings; MCMC Reversible Jump; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE E ESTATISTICA APLICADAS; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::PROCESSOS MARKOVIANOS