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

Area of Science:

• Chemical Engineering
• Statistics
• Regression Analysis

Background:

• Oil refinery processes involve complex chemical reactions and measurements.
• Catalyst crystallinity and reagent concentration are key variables.
• Existing models may not adequately handle measurement errors in covariates.

Purpose of the Study:

• To propose a general class of nonlinear beta regression models incorporating measurement errors.
• To address the challenge of a reagent concentration covariate measured with error in an oil refinery process.
• To evaluate different parameter estimation methods for the proposed model.

Main Methods:

• Development of a nonlinear beta regression model allowing for measurement errors in the main covariate.
• Estimation of model parameters using various statistical methods.
• Monte Carlo simulations to assess the performance of point and interval estimators.

Main Results:

• The proposed nonlinear beta model effectively handles measurement errors in the chemical reagent concentration.
• Maximum pseudo-likelihood approximation demonstrated superior performance for parameter estimation.
• Simulation results and the refinery process application favored this estimation method.

Conclusions:

• Nonlinear beta regression models with measurement error correction are suitable for analyzing chemical process data.
• Maximum pseudo-likelihood approximation is a robust and reliable method for parameter estimation in these models.
• The developed methodology provides improved insights into oil refinery processes with error-prone measurements.