Measuring overfitting and mispecification in nonlinear models
We start by proposing a new measure of overfitting expressed on the untransformed scale of the dependent variable, which is generally the scale of interest to the analyst.We then show that with nonlinear models shrinkage due to overfitting gets confounded by shrinkage—or expansion— arising from model misspecification. Out-of-sample predictive calibration can in fact be expressed as in-sample calibration times 1 minus this new measure of overfitting. We finally argue that re-calibration should be performed on the scale of interest and provide both a simulation study and a real-data illustration based on health care expenditure data.
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- Willard G. Manning & John Mullahy, 1999.
"Estimating Log Models: To Transform or Not to Transform?,"
NBER Technical Working Papers
0246, National Bureau of Economic Research, Inc.
- Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
- Anirban Basu & Bhakti V. Arondekar & Paul J. Rathouz, 2006. "Scale of interest versus scale of estimation: comparing alternative estimators for the incremental costs of a comorbidity," Health Economics, John Wiley & Sons, Ltd., vol. 15(10), pages 1091-1107.
- Willard G. Manning & Anirban Basu & John Mullahy, 2003.
"Generalized Modeling Approaches to Risk Adjustment of Skewed Outcomes Data,"
NBER Technical Working Papers
0293, National Bureau of Economic Research, Inc.
- Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
- Willard G. Manning & Anirban Basu & John Mullahy, 2003. "Generalized Modeling Approaches to Risk Adjustment of Skewed Outcomes Data," Working Papers 0313, Harris School of Public Policy Studies, University of Chicago.
- Blough, David K. & Madden, Carolyn W. & Hornbrook, Mark C., 1999. "Modeling risk using generalized linear models," Journal of Health Economics, Elsevier, vol. 18(2), pages 153-171, April.
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