In rdrr1990/bigKRLS: Optimized Kernel Regularized Least Squares

This little demo shows how to use and interpret crossvalidate.bigKRLS on the Boston housing data. (medv is median house value).

knitr::opts_chunk$set(comment="")

library(pacman)
p_load(bigKRLS, tidyverse, knitr, MASS)
opts_chunk$set(tidy = TRUE, comment = "")

glimpse(Boston)

y <- as.matrix(Boston$medv)
X <- as.matrix(Boston %>% dplyr::select(-medv))

out <- crossvalidate.bigKRLS(y, X, seed = 1234, Kfolds = 5)

s <- summary(out)
s[["overview"]]

| |Fold 1 |Fold 2 |Fold 3 |Fold 4 |Fold 5 | |:-----------------------|:-------|:--------|:--------|:-------|:-------| |MSE (In Sample) |5.547 |5.339 |5.332 |4.303 |5.504 | |MSE (Out of Sample) |8.464 |10.896 |8.970 |17.715 |7.753 | |MSE AME (In Sample) |815.101 |1388.626 |1080.492 |489.638 |801.770 | |MSE AME (Out of Sample) |754.644 |1724.905 |1328.164 |392.617 |753.858 | |R2 (In Sample) |0.937 |0.938 |0.940 |0.944 |0.935 | |R2 (Out of Sample) |0.883 |0.868 |0.871 |0.857 |0.910 | |R2 AME (In Sample) |0.068 |0.048 |0.070 |0.046 |0.068 | |R2 AME (Out of Sample) |0.085 |0.120 |0.019 |0.356 |0.108 |

The predictiveness of the model is relatively stable across models (85-90% of variance explained). The model fits the best for Fold 5 (lowest Mean Squared Error and highest $R^2$ out of sample). The model is massively non-additive in that giant gaps between how much the model as a whole explains vs. how much the average marginal effects (AMEs) explain. Put differently, most of the variance is explained by interactions. The AMEs are most informative for Fold 4.