Marginally restricted D-optimal designs for correlated observations

Abstract

Two practical degrees of complexity may arise when designing an experiment for a model of a real life case. First, some explanatory variables may not be under the control of the practitioner. Secondly, the responses may be correlated. In this paper three real life cases in this situation are considered. Different covariance structures are studied and some designs are computed adapting the theory of marginally restricted designs for correlated observations. An exchange algorithm given by Brimkulov's algorithm is also adapted to marginally restricted D–optimality and it is applied to a complex situation.

Keywords:

• exact design
• covariance structure
• exchange algorithm

AMS Subject Classification:

• 62k05

Acknowledgements

This work was undertaken under the financial support of Acciones Integradas (HU 2003-0026), Ministerio de Educación y Ciencia MTM2007 67211 C3-01 and Junta de Comunidades de Castilla-La Mancha PAI07-0019-2036. The third author was also supported by the FWF-grant P16809-N2 (Austrian grant agency) and by the VEGA grant no. 1/3016/06 (Slovak grant agency). The authors warmly acknowledge G. Sánchez-León, I. Ballesteros and ENUSA factory for providing us with real life data and suggesting the models used in Sections 4 and 6.