discrim_flexible() is a way to generate a specification of a flexible discriminant model using features created using multivariate adaptive regression splines (MARS).

discrim_flexible(
mode = "classification",
num_terms = NULL,
prod_degree = NULL,
prune_method = NULL
)

# S3 method for discrim_flexible
update(
object,
num_terms = NULL,
prod_degree = NULL,
prune_method = NULL,
fresh = FALSE,
...
)

## Arguments

mode A single character string for the type of model. The only possible value for this model is "classification". The number of features that will be retained in the final model, including the intercept. The highest possible interaction degree. The pruning method. A flexible discriminant model specification. A logical for whether the arguments should be modified in-place of or replaced wholesale. Not used for update().

## Details

Flexible discriminant analysis (FDA) uses the work of Hastie et al (1994) to create a discriminant model using different feature expansions. For this function, MARS (Friedman, 1991) hinge functions are used to nonlinearly model the class boundaries (see example below). The mda and earth packages are needed to fit this model.

The main arguments for the model are:

• num_terms: The number of features that will be retained in the final model.

• prod_degree: The highest possible degree of interaction between features. A value of 1 indicates and additive model while a value of 2 allows, but does not guarantee, two-way interactions between features.

• prune_method: The type of pruning. Possible values are listed in ?earth.

These arguments are converted to their specific names at the time that the model is fit. Other options and argument can be set using set_engine(). If left to their defaults here (NULL), the values are taken from the underlying model functions. If parameters need to be modified, update() can be used in lieu of recreating the object from scratch.

The model can be created using the fit() function using the following engines:

• R: "earth" (the default)

## Engine Details

Engines may have pre-set default arguments when executing the model fit call. For this type of model, the template of the fit calls are:

discrim_flexible() %>%
set_engine("earth") %>%
translate()

## Flexible Discriminant Model Specification (classification)
##
## Computational engine: earth
##
## Model fit template:
## mda::fda(formula = missing_arg(), data = missing_arg(), method = earth::earth)

The standardized parameter names in parsnip can be mapped to their original names in each engine that has main parameters. Each engine typically has a different default value (shown in parentheses) for each parameter.

 parsnip earth num_terms nprune (all created by forward pass) prod_degree degree (1) prune_method pmethod (backward)

## References

Friedman (1991), Multivariate Adaptive Regression Splines (with discussion), Annals of Statistics 19:1, 1–141. Hastie, Tibshirani and Buja (1994), Flexible Discriminant Analysis by Optimal Scoring, Journal of the American Statistical Association, 1255-1270.

## Examples

parabolic_grid <-
expand.grid(X1 = seq(-5, 5, length = 100),
X2 = seq(-5, 5, length = 100))

fda_mod <-
discrim_flexible(num_terms = 3) %>%
# increase num_terms to find smoother boundaries
set_engine("earth") %>%
fit(class ~ ., data = parabolic)

parabolic_grid$fda <- predict(fda_mod, parabolic_grid, type = "prob")$.pred_Class1

library(ggplot2)
ggplot(parabolic, aes(x = X1, y = X2)) +
geom_point(aes(col = class), alpha = .5) +
geom_contour(data = parabolic_grid, aes(z = fda), col = "black", breaks = .5) +
theme_bw() +
theme(legend.position = "top") +
coord_equal()

model <- discrim_flexible(num_terms = 10)
model#> Flexible Discriminant Model Specification (classification)
#>
#> Main Arguments:
#>   num_terms = 10
#> update(model, num_terms = 6)#> Flexible Discriminant Model Specification (classification)
#>
#> Main Arguments:
#>   num_terms = 6
#>