Study of the best designs for modifications of the Arrhenius equation

The Arrhenius equation is widely used to describe the relationship between the rate of a chemical reaction and the temperature. However, in some cases more precision is needed and a Modified Arrhenius (MA) model, allowing the linear parameter to be temperature-dependent, appears as the correct alternative to the plain model. Optimal designs for the Arrhenius equation have been already computed, for instance in Rodríguez-Aragón and López Fidalgo [L.J. Rodríguez-Aragón and J. López-Fidalgo (2005). Optimal designs for the Arrhenius equation. Chemometr Intell Lab Syst 77 131–138.] for independent and normally-distributed errors with constant variance and in Rodríguez-Torreblanca and Rodríguez-Díaz [C. Rodríguez-Torreblanca and J.M. Rodríguez Díaz (2007). Locally D- and c-optimal designs for Poisson and Negative Binomial regression models. Metrika 66 161–172.] for different variance structures. However, the MA model has not been studied at the same level. In this work, optimal designs for this last equation will be computed for a general design space and different optimality criteria, and their performance will be shown through convenient examples. A robustness analysis when a wrong choice of the initial values for the parameters is made or some of the hypothesis on the model are not fulfilled will be performed, in order to be able to choose the best design for each situation.