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It’s Appendix A of ARM:
A.1. Fit many models
Think of a series of models, starting with the too-simple and continuing through to the hopelessly messy. Generally it’s a good idea to start simple. Or start complex if you’d like, but prepare to quickly drop things out and move to the simpler model to help understand what’s going on. Working with simple models is not a research goal—in the problems we work on, we usually find complicated models more believable—but rather a technique to help understand the fitting process.
A corollary of this principle is the need to be able to fit models relatively quickly. Realistically, you don’t know what model you want to be fitting, so it’s rarely a good idea to run the computer overnight fitting a single model. At least, wait until you’ve developed some understanding by fitting many models.
A.2. Do a little work to make your computations faster and more reliable
This sounds like computational advice but is really about statistics: if you can fit models faster, you can fit more models and better understand both data and model. But getting the model to run faster often has some startup cost, either in data preparation or in model complexity.
Data subsetting . . .
Fake-data and predictive simulation . . .
A.3. Graphing the relevant and not the irrelevant
Graphing the fitted model
Graphing the data is fine (see Appendix B) but it is also useful to graph the estimated model itself (see lots of examples of regression lines and curves throughout this book). A table of regression coefficients does not give you the same sense as graphs of the model. This point should seem obvious but can be obscured in statistical textbooks that focus so strongly on plots for raw data and for regression diagnostics, forgetting the simple plots that help us understand a model.
Don’t graph the irrelevant
Are you sure you really want to make those quantile-quantile plots, influence dia- grams, and all the other things that spew out of a statistical regression package? What are you going to do with all that? Just forget about it and focus on something more important. A quick rule: any graph you show, be prepared to explain.
A.4. Transformations
Consider transforming every variable in sight:
• Logarithms of all-positive variables (primarily because this leads to multiplicative models on the original scale, which often makes sense)
• Standardizing based on the scale or potential range of the data (so that coefficients can be more directly interpreted and scaled); an alternative is to present coefficients in scaled and unscaled forms
• Transforming before multilevel modeling (thus attempting to make coefficients more comparable, thus allowing more effective second-level regressions, which in turn improve partial pooling).
Plots of raw data and residuals can also be informative when considering transformations (as with the log transformation for arsenic levels in Section 5.6).
In addition to univariate transformations, consider interactions and predictors created by combining inputs (for example, adding several related survey responses to create a “total score”). The goal is to create models that could make sense (and can then be fit and compared to data) and that include all relevant information.
A.5. Consider all coefficients as potentially varying
Don’t get hung up on whether a coefficient “should” vary by group. Just allow it to vary in the model, and then, if the estimated scale of variation is small (as with the varying slopes for the radon model in Section 13.1), maybe you can ignore it if that would be more convenient.
Practical concerns sometimes limit the feasible complexity of a model—for example, we might fit a varying-intercept model first, then allow slopes to vary, then add group-level predictors, and so forth. Generally, however, it is only the difficulties of fitting and, especially, understanding the models that keeps us from adding even more complexity, more varying coefficients, and more interactions.
A.6. Estimate causal inferences in a targeted way, not as a byproduct of a large regression
Don’t assume that a regression coefficient can be interpreted causally. If you are interested in causal inference, consider your treatment variable carefully and use the tools of Chapters 9, 10, and 23 to address the difficulties of comparing comparable units to estimate a treatment effect and its variation across the population. It can be tempting to set up a single large regression to answer several causal questions at once; however, in observational settings (including experiments in which certain conditions of interest are observational), this is not appropriate, as we discuss at the end of Chapter 9.
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