This is the first of several connected topics organized around chapters in Regression Modeling Strategies. The purposes of these topics are to introduce key concepts in the chapter and to provide a place for questions, answers, and discussion around the chapter’s topics.
Overview | Course Notes
Key points featured in Chapter 1:
- The regression modeling framework for statistical analysis accommodates all the fundamental statistical interests of estimation, hypothesis testing, description, bias mitigation, and prediction;
- The ultimate measure of statistical veridicality is “accurate prediction of responses for future observations”—so all inferential statistical objectives are optimized in as much as model predictions are performant;
- Every hypothesis test implies a model—and models, moreover, make many of the underlying assumptions of hypothesis tests explicit;
- It is advantageous to approach effect estimation from a model as differences in predicted values;
- For comparison of responses or outcomes among groups, multivariable models are important—even for randomized designs;
- It is important to distinguish prediction and classification—and predictions should be separate from decisions so as not to distort and compromise either the prediction or the decision (see also Classification vs. Prediction and Damage Caused by Classification Accuracy and Other Discontinuous Improper Accuracy Scoring Rules);
- Development of the most accurate and reliable predictive model will enhance any/all of an analysts’ research interests;
- There are many ways and reasons that developing a model which will yield accurate and reliable predictions can go awry, but a principle-based approach guiding empirical model development can be felicitous;
- A principal-principle is, for an efficient and valid analysis, thoughtful selection of a response variable that is faithful to the nature of—and information in—the problem is crucial (see BBR notes 3.4.1. Proper Response Variables);
- And, finally, ‘friends don’t let friends’ categorize continuous response variables!
Written by @Drew_Levy