The simulated examples are constructed to demonstrate properties of predictive comparisons in artificial simulations that we can perfectly understand (because we created them).
Logistic regression for wine prices: This is a logistic regression model run in different simulated data situations. Changing the relationship between the inputs (and nothing else) leads to differences in the predictive comparisons, despite the logistic regression model remaining the same.
Linear model with interactions: This is a linear model with 9 features and 8 interaction terms (an interaction between \(v\) and each of \(u_1 \ldots u_8\)) which are all the same. The way the \(u_i\)'s are related to \(v\) in the distribution of the inputs gives rise to differences in the APC, despite each \(u_i\) playing the same role in the model.
Simulated examples are good for gaining understanding of how the package works and what it's doing, but they don't help us understand how it is useful in the real world. These are examples with real-world data sets: