A New Generalization of Neyman's Smooth Test and Its Application to Testing Binary Response GLM Goodness of Link

• Activity Number: 209
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mark H. Inlow*+
• Companies: University of Arizona
• Keywords: logistic regression ; goodness of link ; GLM ; lack of fit ; smooth test ; binary response

Abstract

We present a new generalization of Neyman's smooth test to the composite case in which we want to determine if the generating process for the data is adequately described by a particular parametric model. The key principle of Neyman's smooth test is to embed the model under consideration within a larger (extended) parametric family providing models which depart "smoothly" from the null model. The adequacy of the null model is then ascertained by using the extended family to generate a score test. Our new generalization is able to adhere more closely to the spirit of Neyman's original smooth test by generating the extended family in an adaptive manner. We use our new smooth test generalization to develop new goodness-of-link tests for binary response GLM's, e.g., logistic regression models. We present simulation studies which show these tests compare very favorably with current methods, some of which are traditional smooth tests.