Approximate local influence in generalized linear mixed models

• Autor(a) principal: Noguera, Sergio Alexander Gomez
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-05022020-190820/
• topic: Aproximação de Laplace; Conformal normal curvature; Curvatura normal conformal; Efeitos aleatórios; Esquema de perturbação; Generalized linear mixed model; Indivíduos influentes; Influência local; Influential observations; Influential subjects; Laplace approximation; Local influence; Modelo linear generalizado misto; Observações influentes; Perturbation scheme; Random effects

Non-Gaussian correlated data are frequent in longitudinal and repeated measure studies. Generalized linear mixed models (GLMMs) are a powerful tool for the analysis and treatment of this kind of data. Residual and sensitivity analysis are useful diagnostic procedures to verify the assumptions made on these models and the adequacy to the data. Among the techniques included in the sensitivity analysis is the local influence, which allows to discriminate observations with a undue weight in the parameter estimates of any statistical model. In this work we present approximated analytical structures for local influence measurements in generalized linear mixed models. These structures were obtained through Laplace approximations for usual perturbation schemes in order to discriminate observations and subjects with excessive influence on the parameter estimates. These measures, which are presented in closed forms for the generalized linear mixed models, have a relatively low computational cost and have been shown to be effective in detection of influential observations and subjects as evidenced by simulation studies and analyses of three real data sets.