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Robustness of design for the testing of lack of fit and for estimation in binary response models

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  • Wiens, Douglas P.

Abstract

Experimentation in scientific or medical studies is often carried out in order to model the 'success' probability of a binary random variable. Experimental designs for the testing of lack of fit and for estimation, for data with binary responses depending upon covariates which can be controlled by the experimenter, are constructed. It is supposed that the preferred model is one in which the probability of the occurrence of the target outcome depends on the covariates through a link function (logistic, probit, etc.) evaluated at a regression response -- a function of the covariates and of parameters to be estimated from the data, once gathered. The fit of this model is to be tested within a broad class of alternatives over which the regression response varies. To this end, the problem is phrased as one of discriminating between the preferred model and the class of alternatives. This, in turn, is a hypothesis testing problem, for which the asymptotic power of the test statistic is directly related to the Kullback-Leibler divergence between the models, averaged over the design. 'Maximin' designs, which maximize (through the design) the minimum (among the class of alternative models) value of this power together with a measure of the efficiency of the parameter estimates are also constructed. Several examples are presented in detail; two of these relate to a medical study of fluoxetine versus a placebo in depression patients. The method of design construction is computationally intensive, and involves a steepest descent minimization routine coupled with simulated annealing.

Suggested Citation

  • Wiens, Douglas P., 2010. "Robustness of design for the testing of lack of fit and for estimation in binary response models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3371-3378, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3371-3378
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    References listed on IDEAS

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    1. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.
    2. Bischoff, Wolfgang & Miller, Frank, 2006. "Lack-of-fit-efficiently optimal designs to estimate the highest coefficient of a polynomial with large degree," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1701-1704, September.
    3. Wiens, Douglas P., 1991. "Designs for approximately linear regression: two optimality properties of uniform designs," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 217-221, September.
    4. Adewale, Adeniyi J. & Wiens, Douglas P., 2006. "New criteria for robust integer-valued designs in linear models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 723-736, November.
    5. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
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    Cited by:

    1. Dette, Holger & Melas, Viatcheslav B. & Shpilev, Petr, 2017. "T-optimal discriminating designs for Fourier regression models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 196-206.

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