In this study we develop a new method for testing the null hypothesis that the predictor
function in a canonical link regression model has a prescribed linear form. The class of
models, which we will refer to as canonical link regression models, constitutes arguably
the most important subclass of generalized linear models and includes several of the most
popular generalized linear models. In addition to the primary contribution of this study,
we will revisit several other tests in the existing literature. The common feature among the
proposed test, as well as the existing tests, is that they are all based on orthogonal series
estimators and used to detect departures from a null model.
Our proposal for a new lack-of-fit test is inspired by the recent contribution of Hart
and is based on a Laplace approximation to the posterior probability of the null hypothesis.
Despite having a Bayesian construction, the resulting statistic is implemented in a
frequentist fashion. The formulation of the statistic is based on characterizing departures
from the predictor function in terms of Fourier coefficients, and subsequent testing that all
of these coefficients are 0. The resulting test statistic can be characterized as a weighted
sum of exponentiated squared Fourier coefficient estimators, whereas the weights depend
on user-specified prior probabilities. The prior probabilities provide the investigator the
flexibility to examine specific departures from the prescribed model. Alternatively, the use
of noninformative priors produces a new omnibus lack-of-fit statistic.
We present a thorough numerical study of the proposed test and the various existing
orthogonal series-based tests in the context of the logistic regression model. Simulation
studies demonstrate that the test statistics under consideration possess desirable power
properties against alternatives that have been identified in the existing literature as being
important.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2011-05-9173 |
| Date | 2011 May 1900 |
| Creators | Glab, Daniel Laurence |
| Contributors | Wehrly, Thomas E. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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