A simple and general goodness-of-fit methodology for regression models

• Ano de defesa: 2022
• Autor(a) principal: Arruda, Helder Alves
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Coefficient of determination; Coeficiente de determinação; Diagnostic; Diagnóstico; Falta de ajuste; Hypothesis test; Intervalos de predição; Lack-of-fit; Model checking; Performance; Prediction intervals; Teste de hipóteses; Verificação do modelo
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-28062022-215419/

The creation of statistical models comes from the need to try to understand phenomena around us. In order to achieve these goals, it is necessary to make assumptions about the problem; therefore, as important as the creation of models is the verification that the assumptions made are plausible. This thesis\'s objective was to create a new methodology for the diagnosis of regression models. It is based on obtaining prediction intervals for new observations under the null hypothesis and averaging the absolute differences between the observed and expected coverage of these intervals; we denote the resulting statistic Mn. If the model specifications are reasonable, we expect values of Mn close to 0. In principle, the only assumption made for using the methodology is independence and the continuous response of the observations. However, an adaptation for the count data case based on randomization was also developed. In both situations, we present theoretical results about Mn and conduct tests through applications, simulations, and comparisons with other goodness-of-fit methodologies in the literature. We concluded that our methodology presented satisfactory results, proving to be very promising and applicable to the most diverse types of regression models.