Robust designs for misspecified logistic models

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Journal of Statistical Planning and Inference (Impact Factor: 0.68). 01/2009; 139(1):3-15. DOI: 10.1016/j.jspi.2008.05.022
Source: OAI


We develop criteria that generate robust designs and use such criteria for the construction of designs that insure against possible misspecifications in logistic regression models. The design criteria we propose are different from the classical in that we do not focus on sampling error alone. Instead we use design criteria that account as well for error due to bias engendered by the model misspecification. Our robust designs optimize the average of a function of the sampling error and bias error over a specified misspecification neighbourhood. Examples of robust designs for logistic models are presented, including a case study implementing the methodologies using beetle mortality data.

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Available from: Douglas P. Wiens, Oct 24, 2014
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    • "Adewale and Wiens (2009) considered robustness of design for logistic models in which the parametric part of the response is possibly incorrectly assumed to be linear in the regressors. Adewale and Xu (2009) obtained generalized linear model designs that are robust against, among others, parametric departures from the fitted link. Dette et al. (2008) considered the problem of finding the 'minimum effective dose' to yield a particular response. "
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    • "However, a key difference between the literature on optimal design theory in statistics (e.g., Silvey 1980; Atkinson and Donev 1992; Pukelsheim 2006) and the DCE literature, is that the assumptions made in order to derive optimal design results are usually more clearly stated as papers in statistics tend to start with a set of assumptions (not necessarily realistic) and derive results given that set of assumptions. 4 Robustness issues to a range of misspecification issues also receive more attention (Sitter 1992; Adewale and Wiens 2009). 5 We suggest that greater familiarity with this literature should lead to improvements in clarity of communication of optimal design results in the economics, marketing and transportation literature. "
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    • "In addition, Wiens and Xu (2008) discuss the construction of robust Q-optimal static designs for a possibly misspecified nonlinear model. Adewale and Wiens (2009) recently consider robust Q-optimal designs for logistic models with an eye on possible misspecification in the fixed effects specified through the linear predictor. The current work goes beyond that of Wiens and Xu (2008) in that the designs obtained are exact so that they can be implemented by practitioner without further computation and approximation. "
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    ABSTRACT: We discuss robust designs for generalized linear models with protection for possible departures from the usual model assumptions. Besides possible inaccuracy in an assumed linear predictor, both problems of overdispersion and misspecification in link function are addressed. For logistic and Poisson models, as examples, we incorporate the variance function prescribed by a superior model similar to a generalized linear mixed model to address overdispersion, and adopt a parameterized generalized family of link functions to deal with the problem of link misspecification. The design criterion is the average mean squared prediction error (AMSPE). The exact optimal design, which minimizes the AMSPE, is also presented using examples on the toxicity of ethylene oxide to grain beetles, and on Ames Salmonella Assay.
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