Beta regression model nonlinear in the parameters with additive measurement errors in variables

PLoS One. 2021 Jul 29;16(7):e0254103. doi: 10.1371/journal.pone.0254103. eCollection 2021.

Abstract

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biometry*
  • Data Interpretation, Statistical
  • Likelihood Functions
  • Linear Models
  • Monte Carlo Method
  • Nonlinear Dynamics

Grants and funding

This study was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) (https://www.capes.gov.br/), received by DBT through a PhD Scholarship. No additional external funding was received for this study.