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Doctoral Thesis
DOI
10.11606/T.45.2009.tde-29092009-195316
Document
Author
Full name
German Moreno Arenas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Singer, Julio da Motta (President)
Andrade Filho, Mário de Castro
Bolfarine, Heleno
Ferraz, Cristiano
Vieira, Marcel de Toledo
Title in Portuguese
Modelos mistos para populações finitas com erros de medida endógenos e exógenos
Keywords in Portuguese
BLUE
BLUP
Erros de medida
Modelos mistos
População finita.
Abstract in Portuguese
Consideramos a predição ótima de valores latentes com base em dados sujeitos a erros de medida endógenos e exógenos, obtidos a partir de uma amostra aleatória de uma população finita. Consideramos o modelo misto para populações finitas (MMPF) com erros de medida exógenos e endógenos usando o enfoque proposto por Stanek et al. (2004) e Stanek & Singer (2004), e calculamos o melhor preditor linear não enviesado (BLUP) do valor latente da i-ésima unidade selecionada na amostra. Quando as variâncias endógenas são heterocedásticas, o preditor obtido sob o MMPF é diferente do preditor obtido sob o modelo misto usual, pois a constante de encolhimento depende da média das variâncias individuais. Utilizamos simulação para comparar o preditor obtido sob o modelo misto usual (utilizado conforme a interpretação usual) com o preditor obtido sob o MMPF, mostrando que apesar do primeiro ser enviesado, ele geralmente apresenta erro quadrático médio (EQM) menor (ou ligeiramente maior) do que aquele obtido sob o MMPF. Adicionalmente, mostramos como utilizar dois pacotes de \emph estatístico (Proc MIXED do SAS e lme(nlme) do R), construídos sob o modelo misto usual, para ajustar corretamente modelos em situações com erros exógenos e endógenos, heterocedásticos ou homocedásticos.
Title in English
Finite population mixed models with endogenous and exogenous measurement errors
Keywords in English
BLUE
BLUP
Finite population
Measurement errors
Mixed models
Abstract in English
We consider optimal estimation and prediction of latent values based on data subject to endogenous and exogenous measurement errors, obtained via simple random sample from a finite population. We consider a finite population mixed model (FPMM) with endogenous and exogenous measurement errors proposed by Stanek III et al. (2004) and Stanek III & Singer (2004) and obtained the best linear unbiased predictor (BLUP) of the latent value of the i-th unit selected in the sample. When the endogenous variances are heteroscedastic, the predictor obtained under the FPMM is different than the predictor obtained with the usual mixed model, because the shrinkage constant depends on the average of the individual variances. We consider simulation studies to compare the predictor obtained under the usual mixed model (used according to the usual interpretation) with the predictor obtained under the FPMM, and show that the former is biased, but usually presents smaller (or slightly larger) mean squared error (MSE) than the predictor obtained under the FPMM. Additionally, we indicate how two commonly used statistical software packages (SAS's Proc MIXED and R's lme(nlme) ) may be employed to fit mixed models in situations with heteroscedastic or homoscedastic exogenous and endogenous errors.
 
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GMATese.pdf (32.58 Mbytes)
Publishing Date
2009-11-19
 
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