Tests for the response distribution in a Poisson regression model

A test of fit of a Poisson regression model to a set of data is composite, with two components: the test that the regression model is correct, and the test that the response has a Poisson distribution. Here, we give tests which are effective for the second assumption. The tests are based on the resi...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2002-11, Vol.108 (1), p.137-154
Main Authors: Spinelli, John J., Lockhart, Richard A., Stephens, Michael A.
Format: Article
Language:English
Subjects:
Applications
Cramér–von Mises statistics
Discrete data
Exact sciences and technology
Generalized linear model
Goodness-of-fit
Linear inference, regression
Mathematics
Medical sciences
Nonparametric inference
Poisson regression
Probability and statistics
Sciences and techniques of general use
Statistics
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Summary:A test of fit of a Poisson regression model to a set of data is composite, with two components: the test that the regression model is correct, and the test that the response has a Poisson distribution. Here, we give tests which are effective for the second assumption. The tests are based on the residuals after the model has been fitted, and the statistics are Cramér–von Mises statistics. Formulas are given to calculate the statistics, and a combination of asymptotic theory and Monte Carlo methods is used to find the estimated p-value of the test statistic. An example is given involving cancer data for workers at an aluminum plant. Power comparisons are made with other tests for the Poisson regression model. The results show that the statistics are good overall against alternatives to the Poisson assumption.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(02)00275-6