  In this paper optimal experimental designs for inverse quadratic regression
models are determined. We consider two different parameterizations of the model
and investigate local optimal designs with respect to the $c$-, $D$- and
$E$-criteria, which reflect various aspects of the precision of the maximum
likelihood estimator for the parameters in inverse quadratic regression models.
In particular it is demonstrated that for a sufficiently large design space
geometric allocation rules are optimal with respect to many optimality
criteria. Moreover, in numerous cases the designs with respect to the different
criteria are supported at the same points. Finally, the efficiencies of
different optimal designs with respect to various optimality criteria are
studied, and the efficiency of some commonly used designs are investigated.
