Smooth tests of goodness of fit for the distributional assumption of regression models

Summary We focus on regression models that consist of (i) a model for the conditional mean of the outcome and (ii) a distributional assumption about the distribution of the outcome, both conditional on the regressors. Generalised linear models form a well‐known example. The choice of the outcome dis...

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Bibliographic Details
Published in:Australian & New Zealand journal of statistics 2022-03, Vol.64 (1), p.67-85
Main Authors: Rayner, J. C. W., Rippon, Paul, Suesse, Thomas, Thas, Olivier
Format: Article
Language:English
Subjects:
GLM
Goodness of fit
model diagnostics
Parameter estimation
Poisson regression
Regression models
score test
Statistical tests
ZIP regression
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Summary:Summary We focus on regression models that consist of (i) a model for the conditional mean of the outcome and (ii) a distributional assumption about the distribution of the outcome, both conditional on the regressors. Generalised linear models form a well‐known example. The choice of the outcome distribution is often motivated by prior or background knowledge of the researcher, or it is simply chosen for convenience. We propose smooth goodness of fit tests for testing the distributional assumption in regression models. The tests arise from embedding the regression model in a smooth family of alternatives, and constructing appropriate score tests that correctly account for nuisance parameter estimation. The tests are customised, focussed and comprehensive. We present several examples to illustrate the wide applicability of our method. A small simulation study demonstrates that our tests have power to detect important deviations from the hypothesised model.
ISSN:1369-1473
1467-842X
DOI:10.1111/anzs.12361