One predictor partial dependence plots for MARS^® Regression

Assume there are m predictors in a training data set, denoted as X₁, X₂, ..., X_m. First, sort the distinct values of predictor X₁ in the training data set in increasing order. Denote x₁₁ as the first distinct value of X₁. Denote x_1N as the last distinct value of X₁. Then, x₁₁ is the x-coordinate for the leftmost point on the plot.

Also suppose that the model has the following regression equation:

Y = 1000 - 5 * BF1 + 3 * BF2

Last, suppose that x₁₁ = 400 and that the minimum fit of the evenly distributed points is 100.

To find the y-coordinate for a partial dependence plot for X₁, consider only the basis functions that involve X₁. Then the fit for x₁₁ that considers only the basis function for X₁ comes from:

1000 − 5 * (max(0, 400 - 350)) = 1000 − 5*50 = 750.

Then the y-coordinate for x₁₁ is 750 - 100 = 650.

Replacing x₁₁ by evenly distributed values from X₁ to X_N, we get the y-coordinates for the rest of the points on the plot. These points allow you to investigate the y-coordinates on the plot in detail. The patterns on the plot are approximately the same as a plot with lines that connect points where the basis functions change. The calculations for the rest of the predictors are done similarly.