Demo

---

• Ames Housing datasets and check rows count

library(AmesHousing)
set.seed(125) 

ames <- make_ames()
ames %>% nrow

## [1] 2930

• Training (70%) and test (30%) sets for the AmesHousing data.

ames_split <- initial_split(ames, prop = .7, strata = "Sale_Price")
ames_train <- training(ames_split)
ames_test  <- testing(ames_split)

• Fit a basic MARS model

mars <- earth(
  Sale_Price ~ .,  
  data = ames_train   
)

• Print model summary

print(mars)

## Selected 39 of 45 terms, and 28 of 307 predictors
## Termination condition: RSq changed by less than 0.001 at 45 terms
## Importance: Gr_Liv_Area, Year_Built, Total_Bsmt_SF, ...
## Number of terms at each degree of interaction: 1 38 (additive model)
## GCV 541517521    RSS 1.030446e+12    GRSq 0.9114527    RSq 0.9178873

summary(mars) %>% .$coefficients %>% head(20)

##                               Sale_Price
## (Intercept)                225296.076852
## h(Gr_Liv_Area-2898)          -609.321128
## h(2898-Gr_Liv_Area)           -51.405211
## h(Year_Built-2003)           2085.245159
## h(2003-Year_Built)           -465.791634
## h(Total_Bsmt_SF-2171)        -625.781911
## h(2171-Total_Bsmt_SF)         -34.308725
## h(1497-Bsmt_Unf_SF)            22.864377
## Overall_QualExcellent       93652.898756
## Overall_QualVery_Excellent 138705.262437
## Overall_QualVery_Good       43195.659866
## h(Kitchen_AbvGr-1)         -19263.659879
## h(Second_Flr_SF-1407)         234.558336
## h(21780-Lot_Area)              -1.807107
## Overall_QualGood            12971.548731
## h(Year_Remod_Add-1970)        513.165148
## h(1970-Year_Remod_Add)        408.113953
## h(Total_Bsmt_SF-2076)         577.301384
## NeighborhoodCrawford        24679.290321
## FunctionalTyp               16804.178157

MARS provide a convenient approach to capture the nonlinearity aspect of polynomial regression by assessing cutpoints (knots) similar to step functions.

• The plot method for MARS model objects provide convenient performance and residual plots

plot(mars, which = 1)

• Model summary capturing GCV \(R^2\) (left-hand y-axis and solid black line) based on the number of terms retained (x-axis) which is based on the number of predictors used to make those terms (right-hand side y-axis).
• For this model, 37 non-intercept terms were retained which are based on 26 predictors.
• Any additional terms retained in the model, over and above these 37, results in less than 0.001 improvement in the GCV \(R^2\)