  Experimental designs for a generalized linear model (GLM) often depend on the
specification of the model, including the link function, the predictors, and
unknown parameters, such as the regression coefficients. To deal with
uncertainties of these model specifications, it is important to construct
optimal designs with high efficiency under such uncertainties. Existing methods
such as Bayesian experimental designs often use prior distributions of model
specifications to incorporate model uncertainties into the design criterion.
Alternatively, one can obtain the design by optimizing the worst-case design
efficiency with respect to uncertainties of model specifications. In this work,
we propose a new Maximin $\Phi_p$-Efficient (or Mm-$\Phi_p$ for short) design
which aims at maximizing the minimum $\Phi_p$-efficiency under model
uncertainties. Based on the theoretical properties of the proposed criterion,
we develop an efficient algorithm with sound convergence properties to
construct the Mm-$\Phi_p$ design. The performance of the proposed Mm-$\Phi_p$
design is assessed through several numerical examples.
