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Beta regression model nonlinear in the parameters with additive measurement errors in variables
Author(s) -
Daniele de Brito Trindade,
Patrícia L. Espinheira,
Klaus L. P. Vasconcellos,
Jalmar M. F. Carrasco,
Maria do Carmo S. Lima
Publication year - 2021
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0254103
Subject(s) - nonlinear regression , nonlinear system , monte carlo method , estimator , errors in variables models , mathematics , covariate , regression analysis , observational error , statistics , mean squared error , computer science , physics , quantum mechanics
We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application concerns a usual oil refinery process where the main covariate is the concentration of a typically measured in error reagent and the response is a catalyst’s percentage of crystallinity involved in the process. Such data have been modeled by nonlinear beta and simplex regression models. Here we propose a nonlinear beta model with the possibility of the chemical reagent concentration being measured with error. The model parameters are estimated by different methods. We perform Monte Carlo simulations aiming to evaluate the performance of point and interval estimators of the model parameters. Both results of simulations and the application favors the method of estimation by maximum pseudo-likelihood approximation.

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