Minimal plus one point designs for testing lack of fit for some sigmoid curve models

D-optimal designs for nonlinear models are often minimally supported. They have been frequently criticized for their inability to test for lack of fit. We construct alternative designs to address this issue for some commonly used sigmoid curves, including logistic, probit, and Gompertz models with two, three, or four parameters. For each model, we compare five nonminimally supported designs in terms of their efficiency, and propose designs that are both statistically efficient and practically convenient for practitioners.