Using regression models for prediction: shrinkage and regression to the mean
- 1 April 1997
- journal article
- Published by SAGE Publications in Statistical Methods in Medical Research
- Vol. 6 (2) , 167-183
- https://doi.org/10.1177/096228029700600206
Abstract
The use of a fitted regression model in predicting future cases, either as a diagnostic tool or as an instrument for risk assessment is discussed. The regression to the mean effect implies that the future values of the response variable tend to be closer to the overall mean than might be expected from the predicted values. The extent of this shrinkage is studied for multiple and logistic regression models, and is found to be related to simple goodness-of-fit statistics of the original regression. Shrinkage is a particularly serious problem if the sample size is small and/or the number of covariates is large. Shrinkage of predictors is illustrated by two examples. A more general formulation is suggested.Keywords
This publication has 9 references indexed in Scilit:
- Predicting Multivariate Responses in Multiple Linear RegressionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1997
- Assessment and Propagation of Model UncertaintyJournal of the Royal Statistical Society Series B: Statistical Methodology, 1995
- Subset Selection in RegressionPublished by Springer Nature ,1990
- Generalized Linear ModelsPublished by Springer Nature ,1989
- On the Robustness of Shrinkage Predictors in Regression to Differences between Past and Future DataJournal of the Royal Statistical Society Series B: Statistical Methodology, 1986
- Regression, Prediction and ShrinkageJournal of the Royal Statistical Society Series B: Statistical Methodology, 1983
- Robust Locally Weighted Regression and Smoothing ScatterplotsJournal of the American Statistical Association, 1979
- Improved Estimators for Coefficients in Linear RegressionJournal of the American Statistical Association, 1968
- Confidence Sets for the Mean of a Multivariate Normal DistributionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1962