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Reference Bands for Nonparametrically Estimated Link Functions |
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| Authors: | Andreas F. Ruckstuhl Alan H. Welsh |
| Affiliation: | 1. Department of Statistics and Econometrics, and Research Fellow, Centre for Mathematics and its Applications , The Australian National University , Canberra , ACT 0200 , Australia;2. Centre for Mathematics and its Applications , The Australian National University , Canberra , ACT 0200 , Australia |
| Abstract: | Abstract We explore the shape of the link function in a generalized linear model by estimating the link nonparametrically. We consider the problem of comparing the nonparametrically estimated link with a particular link function. Using reference bands that consist of pointwise confidence intervals for the nonparametrically estimated link centered at the hypothesized parametric link, simple graphical methods are obtained for comparing the two link functions. The resulting diagnostic plots are demonstrated with both artificial and real examples. |
| Keywords: | Generalized linear model Graphics Local polynomial smoothing |