Decide Variable Type (Iterative)

Description

A stepwise variable-selection method that iteratively chooses each variable's best form: "linear", single-split "dummy", or double-split ("middle=1") dummy, based on AIC/BIC improvement. Supports "forward", "backward", or "both" strategies.

Usage

decide_variable_type_iterative(
  X,
  Y,
  min_support = 0.1,
  min_improvement = 3,
  direction = c("backward", "forward", "both"),
  criterion = c("AIC", "BIC"),
  exclude_vars = NULL,
  verbose = FALSE,
  ...
)

Arguments

Details

By default, no split is allowed with fewer than 5 observations (i.e., minsplit is max(5, ceiling(min_support * n))). This is not user-configurable.

Dummy forms come from a shallow (maxdepth = 2) rpart tree fit to the partial residuals of the current model. We extract up to two splits:

• Single cutoff dummy (e.g., x >= c)

• Double cutoff dummy (e.g., c1 < x < c2)

The function then picks the form (linear, single-split dummy, or double-split dummy) that yields the lowest AIC/BIC. Variables listed in exclude_vars will be forced to remain linear (dummy transformations are never attempted).

Value

A named list of decisions, where each element is a list with:

type

Either "linear" or "dummy".

cutoff

A numeric vector of length 1 or 2 (the chosen split points).

Decide Variable Type (Univariate)

Description

For each numeric predictor, this function fits a shallow (maxdepth = 2) rpart tree directly on Y ~ x and tests whether a dummy transformation improves model fit.

Usage

decide_variable_type_univariate(
  X,
  Y,
  min_support = 0.1,
  min_improvement = 3,
  criterion = c("AIC", "BIC"),
  exclude_vars = NULL,
  verbose = FALSE
)

Arguments

Details

By default, no split is allowed with fewer than 5 observations (i.e., minsplit is max(5, ceiling(min_support * n))). This is not user-configurable.

Dummy forms come from a shallow (maxdepth = 2) rpart tree fit to the data. We extract up to two splits:

• Single cutoff dummy (e.g., x >= c)

• Double cutoff dummy (e.g., c1 < x < c2)

The function then picks the form (linear, single-split dummy, or double-split dummy) that yields the lowest AIC/BIC. If a variable is listed in exclude_vars, it will always be used as a linear predictor (dummy transformation is never attempted).

Value

A named list of decisions, where each element is a list with:

type

Either "dummy" or "linear".

cutoffs

A numeric vector (length 1 or 2) if type = "dummy", or NULL if linear.

tree_model

The fitted rpart model (for reference) or NULL if excluded.

SplitWise Regression

Description

Transforms each numeric variable into either a single-split dummy or keeps it linear, then runs stats::step() for stepwise selection. The user can choose a simpler univariate transformation or an iterative approach.

Usage

splitwise(
  formula,
  data,
  transformation_mode = c("iterative", "univariate"),
  direction = c("backward", "forward", "both"),
  min_support = 0.1,
  min_improvement = 3,
  criterion = c("AIC", "BIC"),
  exclude_vars = NULL,
  verbose = FALSE,
  steps = 1000,
  k = 2,
  ...
)

## S3 method for class 'splitwise_lm'
print(x, ...)

## S3 method for class 'splitwise_lm'
summary(object, ...)

## S3 method for class 'splitwise_lm'
predict(object, newdata, ...)

## S3 method for class 'splitwise_lm'
coef(object, ...)

## S3 method for class 'splitwise_lm'
fitted(object, ...)

## S3 method for class 'splitwise_lm'
residuals(object, ...)

## S3 method for class 'splitwise_lm'
model.matrix(object, ...)

Arguments

Value

An S3 object of class c("splitwise_lm", "lm"), storing:

Functions

• print(splitwise_lm): Prints a summary of the splitwise_lm object.

• summary(splitwise_lm): Provides a detailed summary, including how dummies were created.

• predict(splitwise_lm): Generate predictions from a splitwise_lm object using learned transformation rules.

• coef(splitwise_lm): Extract model coefficients from a SplitWise linear model.

• fitted(splitwise_lm): Extract fitted values from a SplitWise linear model.

• residuals(splitwise_lm): Extract residuals from a SplitWise linear model.

• model.matrix(splitwise_lm): Extract the model matrix from a SplitWise linear model.

Examples

# Load the mtcars dataset
data(mtcars)

# Univariate transformations (AIC-based, backward stepwise)
model_uni <- splitwise(
  mpg ~ .,
  data               = mtcars,
  transformation_mode = "univariate",
  direction           = "backward"
)
summary(model_uni)

# Iterative approach (BIC-based, forward stepwise)
# Note: typically set k = log(nrow(mtcars)) for BIC in step().
model_iter <- splitwise(
  mpg ~ .,
  data               = mtcars,
  transformation_mode = "iterative",
  direction           = "forward",
  criterion           = "BIC",
  k                   = log(nrow(mtcars))
)
summary(model_iter)

Transform Features (Iterative Logic)

Description

Once decide_variable_type_iterative has chosen which variables to add (and how), we can build a final data frame from those decisions.

Usage

transform_features_iterative(X, decisions)

Arguments

Value

A data frame with the chosen variables in their final forms (dummy or linear).

Transform Features (Univariate Logic)

Description

Given the decisions (dummy or linear) for each predictor, produce a transformed data frame. Dummy columns are 0/1 based on the cutoff.

Usage

transform_features_univariate(X, decisions)

Arguments

Value

A new data frame with either the original column or a dummy column for each variable.