Experimental designs for controlling the correlation of estimators in two parameter models

TL;DR

This paper reviews parameter correlation issues in two-parameter models, analyzes conflicting views on D-optimality, and proposes an analytical criterion that improves control over estimator precision and correlation, validated through linear and non-linear models.

Contribution

It introduces a new analytical criterion that simultaneously optimizes estimator precision and reduces correlation, outperforming existing strategies.

Findings

The new criterion outperforms existing methods in controlling correlation.

Validated on linear and non-linear models with strong correlation.

Shows superior performance in both simple and complex models.

Abstract

The state of the art related to parameter correlation in two-parameter models has been reviewed in this paper. The apparent contradictions between the different authors regarding the ability of D--optimality to simultaneously reduce the correlation and the area of the confidence ellipse in two-parameter models were analyzed. Two main approaches were found: 1) those who consider that the optimality criteria simultaneously control the precision and correlation of the parameter estimators; and 2) those that consider a combination of criteria to achieve the same objective. An analytical criterion combining in its structure both the optimality of the precision of the estimators of the parameters and the reduction of the correlation between their estimators is provided. The criterion was tested both in a simple linear regression model, considering all possible design spaces, and in a non-linear model with strong correlation of the estimators of the parameters (Michaelis--Menten) to show its performance. This criterion showed a superior behavior to all the strategies and criteria to control at the same time the precision and the correlation.