Plotting models with more than one input variable

Manuel Spínola writes,

In the book you say that it is a good idea to plot the fitted model. How do you do that when you have, for example, 3 explanatory variables? Or do you mean plotting one variable at the time?

My reply:

I would plot one variable at a time, but then you can use multiple graphs to show different levels of a second variable, and multiple lines per graph to show different levels of a third variable, and solid/dotted lines to show a fourth variable, and a second dimension of a grid of plots to show a fifth, and color to show a sixth. For an example, see Figure 2 of this paper.

I used to like to use different symbols and symbol sizes to add more dimensions, but now I’m happier with “small multiples”–that is, one-way or two-way grids of plots. Sort of like Trellis, except that I like to label the internal axes locally (right on the little graphs) and label the external axes on the outside of the plot (see, for example, Figure 15.7 on page 335 in our book). I find the Trellis convention (using external labels for the internal axes) confusing.

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