These notes by Léo Belzile (HEC Montréal) are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License and were last compiled on 2022-11-23.
While we show how to implement statistical tests and models in SAS in class, these note will illustrate the concepts using R: visit the R-project website to download the program. The most popular graphical cross-platform front-end is RStudio Desktop.
Why use models? Paul Krugman wrote in 2010 in his blog
The answer I’d give is that models are an enormously important tool for clarifying your thought. You don’t have to literally believe your model — in fact, you’re a fool if you do — to believe that putting together a simplified but complete account of how things work, with all the eyes crossed and teas dotted or something, helps you gain a much more sophisticated understanding of the real situation. People who don’t use models end up relying on slogans that are much more simplistic than the models
A famous quote attributed to George Box claims that
All models are wrong, but some are useful.
This standpoint is reductive: Peter McCullagh and John Nelder wrote in the preamble of their book (emphasis mine)
Modelling in science remains, partly at least, an art. Some principles do exist, however, to guide the modeller. The first is that all models are wrong; some, though, are better than others and we can search for the better ones. At the same time we must recognize that eternal truth is not within our grasp.
And this quote by David R. Cox adds to the point:
…it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model.