A novel perspective for parameter estimation of seemingly unrelated nonlinear regression

Modeling hormesis using multivariate nonlinear regression in plant biology: A comprehensive approach to understanding dose-response relationships

For over a century, ecotoxicological studies have reported the occurrence of hormesis as a significant phenomenon in many areas of science. In plant biology, hormesis research focuses on measuring morphological, physiological, biochemical, and productivity changes in plants exposed to low doses of herbicides. These studies involve multiple features that are often correlated. However, the multivariate aspect and interdependencies among components of a plant system are not considered in the adopted modeling framework. Therefore, a multivariate nonlinear modeling approach for hormesis is proposed, where information regarding correlations among response variables is taken into account through a variance-covariance matrix obtained from univariate residuals. The proposed methodology is evaluated through a Monte Carlo simulation study and an application to experimental data from safflower (Carthamus tinctorius L.) cultivation. In the simulation study, the multivariate model outperformed the univariate models, exhibiting higher precision, lower bias, and greater accuracy in parameter estimation. These results were also confirmed in the analysis of the experimental data. Using the delta method, mean doses of interest can be derived along with their associated standard errors. This is the first study to address hormesis in a multivariate context, allowing for a better understanding of the biphasic dose-response relationships by considering the interrelationships among various measured characteristics in the plant system, leading to more precise parameter estimates.