Practical Aspects of the Use of Linear & Generalized Linear Models

Primarily, the purpose of this document is to note issues for the use of linear and generalized linear models, and of other regression models. Worked examples, as far as possible using data that have been a basis for published research, are used as a basis for discussion of the following issues: Missing variables; noting very striking examples that arise in multi-way tables, perhaps modeled using logistic regression; [Maindonald & Braun (2007, Subsections 2.2.1, 3.4.5, 6.8.3 & Section 8.3)] Observational versus experimental data – implications for interpretation and inference; Maindonald & Braun (2007, Chapter 6); Rosenbaum (2002)] Variable selection, noting the use of resampling methods to obtain realistic “error” estimates; [Maindonald & Braun (2007, Chapter 6)] Errors in explanatory variables; implications of classical measurement error for inference; [Maindonald & Braun (2007, Chapter 6); Carroll (2006, Chapter 1)] Regression on constructed variables – propensity scores, with brief mention of principal components and partial least squares; [Maindonald & Braun (2007, Chapter 13)] A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions. M.J.Moroney ∗Centre for Mathematics & Its Applications, Australian National University, Canberra ACT 0200, Australia. mailto:[email protected]