Parallel Slopes Model
Take a look at the parallel slopes model in multiple regression.
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When creating regression models with one numerical and one categorical explanatory variable, we aren’t limited to interaction models, as we just saw. Another type of model we can use is known as a parallel slopes model. Unlike interaction models where the regression lines can have different intercepts and different slopes, parallel slopes models still allow for different intercepts but force all lines to have the same slope. The resulting regression lines are therefore parallel. Let’s visualize the best-fitting parallel slopes model to evals_ch6.
Unfortunately, the geom_smooth() function in the ggplot2 package doesn’t have a convenient way to plot parallel slopes models. Evgeni Chasnovski, therefore, created a special purpose function called geom_parallel_slopes() that’s included in the moderndive package. We won’t find geom_parallel_slopes() in the ggplot2 package, but rather the moderndive package. Thus, if we want to use it, we’ll need to load both the ggplot2 and moderndive packages. Using this function, let’s now plot the parallel slopes model for teaching scores. Notice how the code is identical to the code that produced the visualization of the interaction model, but now the geom_smooth(method = "lm", se = FALSE) layer is replaced with geom_parallel_slopes(se = FALSE).
ggplot(evals_ch6, aes(x = age, y = score, color = gender)) +geom_point() +labs(x = "Age", y = "Teaching Score", color = "Gender") +geom_parallel_slopes(se = FALSE)
Observe in the code output above that we now have parallel lines corresponding to the female and male instructors, respectively, and here they have the same negative slope. This is telling us that instructors who are older will tend to receive lower teaching scores than the instructors who are younger. Furthermore, because the lines are parallel, the associated penalty for being older is assumed to be the same for both female and male instructors.
However, also observe in the code output above that these two lines have different intercepts. This is evident by the fact that the blue line corresponding to the male instructors is higher than the red line corresponding to the female instructors. This tells us that irrespective of age, female instructors tend to receive lower ...