On detecting influential data and selecting regression variables |
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| Affiliation: | 1. Leibniz Institute of Atmospheric Physics at the Rostock University, Schloss-Str. 6, Kühlungsborn 18225, Germany;2. Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada;3. Centre for Planetary Science and Exploration, University of Western Ontario, London, Ontario N6A 5B7, Canada;4. Department of Physics, The Catholic University of America, Washington, DC 20064, USA;5. Space Weather Laboratory, Code 674, NASA Goddard Space Flight Center, Greenbelt, MD 20771, Maryland |
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| Abstract: | The analysis of residuals may reveal various functional forms suitable for the regression model. In this paper, we investigate some selection criteria for selecting important regression variables. In doing so, we use statistical selection and ranking procedures. Thus, we derive an appropriate criterion to measure the influence and bias for the reduced models. We show that the reduced models are based on some noncentrality parameters which provide a measure of goodness of fit for the fitted models. In this paper, we also discuss the relationships of influence diagnostics and the statistic proposed earlier by Gupta and Huang (J. Statist. Plann. Inference 20 (1988) 155–167). We introduce a new measure for detecting influential data as an alternative to Cook's measure. |
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