http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
On techniques for binary response modeling
In this dissertation we contribute to the development of a critical component of binary response modeling, assessment of fit. In particular we develop a new semiparametric method for assessing and correcting lack of fit due to link misspecification, a method we call adaptive smooth tests. Currently, parametric extended models, or families, are used for this purpose. Our new methodology generalizes this approach. We begin by developing a new characterization of Neyman's smooth test. Using this characterization we develop a new, adaptive version of Neyman's smooth test in which the smooth functions on [0,1] defining the alternatives to the null are not specified a priori but are constructed to be optimally smooth, with respect to a roughness penalty, for the sample at hand. Using the fact that Neyman's smooth test statistic is a function only of the smooth functions evaluated at the n sample points, we reduce the problem of generating these functions to an n-dimensional vector optimization problem. Using the comparison distribution approach of Parzen we show that Pregibon's goodness-of-link tests for logistic regression models are smooth tests of fit. Motivated by this fact, we develop several roughness penalties and apply the resulting adaptive smooth tests to simulated binary response data. We show that the power of these tests compares favorably to current tests, equaling and sometimes exceeding the power of the extended model test even when the true model is a member of the extended family.
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Includes bibliographical references (leaves 162-168).