Mixed effects and semi-parametric Bayesian integration models for measurement error correction in the context of fertilizer application levels: a simulation study

Abstract

In agricultural research, the precision of variable measurement is crucial as it forms the foundation for accurate estimations and informed decision-making. However, the presence of measurement errors in real-world data often leads to skewed estimates and flawed conclusions. This study addresses the common challenge of measurement error, focusing on the optimization of fertilizer application levels—a critical factor in sustainable agriculture. Through carefully designed simulation studies, we introduce controlled measurement errors into Gaussian process models and rigorously evaluate their effects on regression outcomes. To strengthen the reliability of our findings, we integrate mixed effects models with a semi-parametric Bayesian framework, leveraging the MCMC Gibbs Sampler for robust inference. Our results highlight the significant impact of measurement errors on the precision of regression estimates, while also demonstrating that advanced statistical models—particularly those combining mixed effects with Bayesian integration—can effectively reduce these errors. This research not only improves the accuracy of agricultural analyses but also offers practical methodologies for optimizing fertilizer use, ultimately contributing to increased agricultural productivity and sustainability. The implications of our findings extend beyond theoretical significance, providing actionable insights that can transform resource management in agricultural practices.