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Title: Probability-based optimal designs to minimise separation Authors:  Steven Gilmour - KCL (United Kingdom) [presenting]
Mohammad Lutfor Rahman - University of Dhaka (Bangladesh)
Abstract: Separation is a common problem in models with binary responses when one or more covariates predict perfectly some binary outcome. Separation is observed during the fitting of logistic models where at least one parameter estimate diverges to infinity. The separation problem leads to convergence difficulties as well as the non-existence of maximum likelihood estimates (MLEs) of model parameters. Researchers are usually advised to deal with separation either by undertaking post hoc data adjustment or by estimation corrections. However, apart from these solutions, the probability of separation arising can be greatly reduced by appropriate design of the experiment. A simple method for doing this is introduced, using newly developed Ps- and DPs- optimality criteria at the design stage. A simple result shows that we should avoid exact replicates, but beyond this, reducing separation and improving parameter estimation are in conflict. We suggest a compound criterion to compromise between these two objectives. Simulation results confirm that the designs produced to achieve the required improvements, and they can be recommended for practical use.