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.Comment: 30 pages, 8 figures, 5 table