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.
Highlights
Regression models for dependent variables that assume values in the unit interval have been proving quite important in the literature, with a special highlight to the beta regression model proposed by [1] and generalized by [2] whom proposed the nonlinear beta regression model
As we shall describe in the application, the measurement of vanadium concentration may be inaccurate, which characterizes the possibility of this covariate to present measurement error
Considering all parameters, measurement errors and sample sizes, this seems to be the recommended method. This is an important aspect, since good estimation of the precision parameters of the observations is directly linked with the efficiency of the estimators and robustness of hypotheses tests about the model parameters
Summary
Regression models for dependent variables that assume values in the unit interval have been proving quite important in the literature, with a special highlight to the beta regression model proposed by [1] and generalized by [2] whom proposed the nonlinear beta regression model. As we shall describe in the application, the measurement of vanadium concentration may be inaccurate, which characterizes the possibility of this covariate to present measurement error. These data were modeled by [5] based on beta and simplex nonlinear regressions in which the vanadium was taken as a fixed covariate. We consider three methods for the estimation of the parameters, namely: approximate maximum likelihood, approximate pseudo maximum likelihood and regression calibration We compare these three methods with the estimation of the naive model, which considers that the regression does not have covariates measured in error, that is, it considers the classical nonlinear beta regression model. Recently [10] proposed the simplex regression models with measurement error, and as a future research we shall extend this proposal to nonlinear case
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