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In the context of nonlinear models, the analytical expression of the Fisher information matrix is essential to compute optimum designs. The Fisher information matrix of the random effects logistic regression model is proved to be equivalent to the information matrix of the linearized model, which depends on some integrals. Some algebraic approximations for these integrals are proposed, which are consistent with numerical integral approximations but much faster to be evaluated. Therefore, thesedoi:10.1016/j.csda.2012.05.024 fatcat:hyrdiqjwnjgjnery3oesybhzee