statisticalrethinkin..

220 7. INTERACTIONSird, we may want to use information criteria or another method to compare models.In order to compare a model that treats all continents the same way to a model that allowsdifferent slopes in different continents, we need models that use all of the same data (asexplained in Chapter 6). is means we can’t split the data, but have to make the model splitthe data.Fourth, once you begin using multilevel models (Chapter 13), you’ll see that there areadvantages to borrowing information across categories like “Africa” and “not Africa.” is isespecially true when sample sizes vary across categories, such that overfitting risk is higherwithin some categories. In other words, what we learn about ruggedness outside of Africashould have some effect on our estimate within Africa, and visa versa. Multilevel modelsborrow information in this way, in order to improve estimates in all categories. When wesplit the data, this borrowing is impossible.So let’s see how to recover the reversal of slope, within a single model.7.1.1. Adding a dummy variable doesn’t work. e first thing to realize is that just includingthe categorical variable (dummy variable) cont_africa won’t reveal the reversed slope.It’s worth fitting this model to prove it to yourself, though. I’m going to walk through thisas a simple model comparison exercise, just so you begin to get some applied examples ofconcepts you’ve accumulated from earlier chapters.e question is to what extent singling out African nations changes predictions. ereare two models to fit, to start. e first is just the simple linear regression of log-GDP onruggedness, but now for the entire data set:R code7.3m7.3