Regression Modeling Strategies

Abstract

There are many books that are excellent sources of knowledge about individual statistical tools (survival models, general linear models, etc.), but the art of data analysis is about choosing and using multiple tools. In the words of Chatfield [100, p. 420] “. . . students typically know the technical details of regression for example, but not necessarily when and how to apply it. This argues the need for a better balance in the literature and in statistical teaching between techniques and problem solving strategies.” Whether analyzing risk factors, adjusting for biases in observational studies, or developing predictive models, there are common problems that few regression texts address. For example, there are missing data in the majority of datasets one is likely to encounter (other than those used in textbooks!) but most regression texts do not include methods for dealing with such data effectively, and most texts on missing data do not cover regression modeling. This book links standard regression modeling approaches with • methods for relaxing linearity assumptions that still allow one to easily obtain predictions and confidence limits for future observations, and to do formal hypothesis tests, • non-additive modeling approaches not requiring the assumption that interactions are always linear × linear, • methods for imputing missing data and for penalizing variances for incomplete data, • methods for handling large numbers of predictors without resorting to problematic stepwise variable selection techniques, • data reduction methods (unsupervised learning methods, some of which are based on multivariate psychometric techniques too seldom used in statistics) that help with the problem of“too many variables to analyze and not enough observations” as well as making the model more interpretable when there are predictor variables containing overlapping information, • methods for quantifying predictive accuracy of a fitted model,