Type:	Package
Title:	A Boosting Approach to Data Envelopment Analysis
Version:	0.1.0
Maintainer:	Maria D. Guillen <maria.guilleng@umh.es>
Description:	Includes functions to estimate production frontiers and make ideal output predictions in the Data Envelopment Analysis (DEA) context using both standard models from DEA and Free Disposal Hull (FDH) and boosting techniques. In particular, EATBoosting (Guillen et al., 2023 <doi:10.1016/j.eswa.2022.119134>) and MARSBoosting. Moreover, the package includes code for estimating several technical efficiency measures using different models such as the input and output-oriented radial measures, the input and output-oriented Russell measures, the Directional Distance Function (DDF), the Weighted Additive Measure (WAM) and the Slacks-Based Measure (SBM).
License:	AGPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.3
Imports:	Rglpk, dplyr, lpSolveAPI, stats, MLmetrics, methods
URL:	https://github.com/itsmeryguillen/boostingDEA
BugReports:	https://github.com/itsmeryguillen/boostingDEA/issues
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
Depends:	R (≥ 3.5.0)
NeedsCompilation:	no
Packaged:	2023-05-15 07:58:20 UTC; Master
Author:	Maria D. Guillen [cre, aut], Juan Aparicio [aut], Víctor España [aut]
Repository:	CRAN
Date/Publication:	2023-05-15 09:10:04 UTC

Add a new pair of Basis Functions

Description

This function adds the best pair of basis functions to the model

Usage

AddBF(data, x, y, ForwardModel, knots_list, Kp, minspan, Le, linpreds, err_min)

Arguments

Value

A list containing the matrix of basis functions (B), a list of basis functions (BF), a list of selected knots (knots_list) and the minimum error (err_min).

Linear programming model for radial input measure

Description

This function predicts the expected output through a DEA model.

Usage

BBC_in(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE
)

Arguments

Value

matrix with the the predicted score

Linear programming model for radial output measure

Description

This function predicts the expected output through a DEA model.

Usage

BBC_out(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE
)

Arguments

Value

matrix with the the predicted score

Single Output Data Generation

Description

This function is used to simulate the data in a single output scenario.

Usage

CobbDouglas(N, nX)

Arguments

Value

data.frame with the simulated data.

Generate a new pair of Basis Functions

Description

This function generates two new basis functions from a variable and a knot.

Usage

CreateBF(data, xi, knt, B, p)

Arguments

Value

Matrix of basis function (B) updated with the new basis functions.

Generate a new pair of Cubic Basis Functions

Description

This function generates two new cubic basis functions from a variable and a knot previously created during MARS algorithm.

Usage

CreateCubicBF(data, xi, knt, B, side)

Arguments

Value

Matrix of basis functions updated with the new basis functions.

Linear programming model for Directional Distance Function measure

Description

This function predicts the expected output through a DEA model.

Usage

DDF(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE,
  direction.vector
)

Arguments

Value

matrix with the the predicted score

Data Envelope Analysis model

Description

This function estimates a production frontier satisfying Data Envelope Analysis axioms using the radial output measure.

This function saves information about the DEA model.

Usage

DEA(data, x, y)

DEA_object(data, x, y, pred, score)

Arguments

Value

A DEA object.

A DEA object.

Efficiency Analysis Trees

Description

This function estimates a stepped production frontier through regression trees.

Usage

EAT(data, x, y, numStop = 5, max.leaves, na.rm = TRUE)

Arguments

Details

The EAT function generates a regression tree model based on CART under a new approach that guarantees obtaining a stepped production frontier that fulfills the property of free disposability. This frontier shares the aforementioned aspects with the FDH frontier but enhances some of its disadvantages such as the overfitting problem or the underestimation of technical inefficiency.

Value

An EAT object containing:

• data

  • df: data frame containing the variables in the model.

  • x: input indexes in data.

  • y: output indexes in data.

  • input_names: input variable names.

  • output_names: output variable names.

  • row_names: rownames in data.

• control

  • fold: fold hyperparameter value.

  • numStop: numStop hyperparameter value.

  • max.leaves: max.leaves hyperparameter value.

  • max.depth: max.depth hyperparameter value.

  • na.rm: na.rm hyperparameter value.

• tree: list structure containing the EAT nodes.

• nodes_df: data frame containing the following information for each node.

  • id: node index.

  • SL: left child node index.

  • N: number of observations at the node.

  • Proportion: proportion of observations at the node.

  • the output predictions.

  • R: the error at the node.

  • index: observation indexes at the node.

• model

  • nodes: total number of nodes at the tree.

  • leaf_nodes: number of leaf nodes at the tree.

  • a: lower bound of the nodes.

  • y: output predictions.

Gradient Tree Boosting

Description

This function estimates a production frontier satisfying some classical production theory axioms, such as monotonicity and determinictiness, which is based upon the adaptation of the machine learning technique known as Gradient Tree Boosting

This function saves information about the EATBoost model

Usage

EATBoost(data, x, y, num.iterations, num.leaves, learning.rate)

EATBoost_object(
  data,
  x,
  y,
  num.iterations,
  num.leaves,
  learning.rate,
  EAT.models,
  f0,
  prediction
)

Arguments

Value

A EATBoost object.

A EATBoost object.

Create a EAT object

Description

This function saves information about the Efficiency Analysis Trees model.

Usage

EAT_object(data, x, y, rownames, numStop, max.leaves, na.rm, tree)

Arguments

Value

An EAT object.

Enhanced Russell Graph measure

Description

This function predicts the expected output through a DEA model.

Usage

ERG(data, x, y, dataOriginal = data, xOriginal = x, yOriginal = y, FDH = FALSE)

Arguments

Value

matrix with the the predicted score

Estimate Coefficients in Multivariate Adaptive Frontier Splines during Forward Procedure.

Description

This function solves a Quadratic Programming Problem to obtain a set of coefficients.

Usage

EstimCoeffsForward(B, y)

Arguments

Value

vector with the coefficients estimated.

Free Disposal Hull model

Description

This function estimates a production frontier satisfying Free Disposal HUll axioms using the radial output measure.

This function saves information about the FDH model.

Usage

FDH(data, x, y)

FDH_object(data, x, y, pred, score)

Arguments

Value

A FDH object.

A FDH object.

Adapted Multivariate Adaptive Frontier Splines

Description

Create an adapted version of Multivariate Adaptive Regression Splines (MARS) model to estimate a production frontier satisfying some classical production theory axioms, such as monotonicity and concavity.

Usage

MARSAdapted(
  data,
  x,
  y,
  nterms,
  Kp = 1,
  d = 2,
  err_red = 0.01,
  minspan = 0,
  endspan = 0,
  linpreds = FALSE,
  na.rm = TRUE
)

Arguments

Value

An AdaptedMARS object.

Smoothing (Forward) Multivariate Adaptive Frontier Splines

Description

This function smoothes the Forward MARS predictor.

Usage

MARSAdaptedSmooth(data, nX, knots, y)

Arguments

Value

List containing the set of knots from backward (knots), the new cubic knots (cubic_knots) and the set of coefficients (alpha).

Create an MARSAdapted object

Description

This function saves information about the adapted Multivariate Adaptive Frontier Splines model.

Usage

MARSAdapted_object(
  data,
  x,
  y,
  rownames,
  nterms,
  Kp,
  d,
  err_red,
  minspan,
  endspan,
  na.rm,
  MARS.Forward,
  MARS.Forward.Smooth
)

Arguments

Value

A MARSAdapted object.

LS-Boosting with adapted Multivariate Adaptive Frontier Splines (MARS)

Description

This function estimates a production frontier satisfying some classical production theory axioms, such as monotonicity and concavity, which is based upon the adaptation of the machine learning technique known as LS-boosting using adapted Multivariate Adaptive Regression Splines (MARS) as base learners.

This function saves information about the LS-Boosted Multivariate Adaptive Frontier Splines model.

Usage

MARSBoost(data, x, y, num.iterations, num.terms, learning.rate)

MARSBoost_object(
  data,
  x,
  y,
  num.iterations,
  learning.rate,
  num.terms,
  MARS.models,
  f0,
  prediction,
  prediction.smooth
)

Arguments

Value

A MARSBoost object.

A MARSBoost object.

Linear programming model for Russell input measure

Description

This function predicts the expected output through a DEA model.

Usage

Russell_in(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE
)

Arguments

Value

matrix with the the predicted score

Linear programming model for Russell output measure

Description

This function predicts the expected output through a DEA model.

Usage

Russell_out(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE
)

Arguments

Value

matrix with the the predicted score

Linear programming model for Weighted Additive Model

Description

This function predicts the expected output through a DEA model.

Usage

WAM(
  data,
  x,
  y,
  dataOriginal = data,
  xOriginal = x,
  yOriginal = y,
  FDH = FALSE,
  weights
)

Arguments

Value

matrix with the the predicted score

Taiwanese banks (in 2010)

Description

The dataset consists of 31 banks operating in Taiwan.

Usage

data(banks)

Format

banks is a dataframe with 31 banks (rows) and 6 variables (outputs) named Financial.funds (deposits and borrowed funds in millions of TWD), Labor (number of employees), Physical.capital (net amount of fixed assets in millions of TWD), Finalcial.investments (financial assets, securities, and equity investments in millions of TWD), Loans (loans and discounts in millions of TWD) and Revenue (interests from financial investments and loans).

Source

The dataset has been extracted from the “Condition and Performance of Domestic Banks” published by the Central Bank of China (Taiwan) and the Taiwan Economic Journal (TEJ) for the year 2010. The “Condition and Performance of Domestic Banks” was downloaded from http://www.cbc.gov.tw/ct.asp?xItem=1062&ctNode=535&mp=2

References

Juo, J. C., Fu, T. T., Yu, M. M., & Lin, Y. H. (2015). Profit-oriented productivity change. Omega, 57, 176-187.

Tuning an EATBoost model

Description

This function computes the root mean squared error (RMSE) for a set of EATBoost models built with a grid of given hyperparameters.

Usage

bestEATBoost(
  training,
  test,
  x,
  y,
  num.iterations,
  learning.rate,
  num.leaves,
  verbose = TRUE
)

Arguments

Value

A data.frame with the sets of hyperparameters and the root mean squared error (RMSE) and mean square error (MSE) associated for each model.

Tuning an MARSBoost model

Description

This funcion computes the root mean squared error (RMSE) for a set of MARSBoost models built with a grid of given hyperparameters.

Usage

bestMARSBoost(
  training,
  test,
  x,
  y,
  num.iterations,
  learning.rate,
  num.terms,
  verbose = TRUE
)

Arguments

Value

A data.frame with the sets of hyperparameters and the root mean squared error (RMSE) associated for each model.

Pareto-dominance relationships

Description

This function denotes if a node dominates another one or if there is no Pareto-dominance relationship.

Usage

comparePareto(t1, t2)

Arguments

Value

-1 if t1 dominates t2, 1 if t2 dominates t1 and 0 if there are no Pareto-dominance relationships.

Deep Efficiency Analysis Trees

Description

This function creates a deep Efficiency Analysis Tree and a set of possible prunings by the weakest-link pruning procedure.

Usage

deepEAT(data, x, y, numStop = 5, max.leaves)

Arguments

Value

A list containing each possible pruning for the deep tree and its associated alpha value.

Calculate efficiency scores

Description

Calculates the efficiency score corresponding to the given model using the given measure

Usage

efficiency(
  model,
  measure = "rad.out",
  data,
  x,
  y,
  heuristic = TRUE,
  direction.vector = NULL,
  weights = NULL
)

Arguments

Value

matrix with the the predicted score

Estimation of child nodes

Description

This function gets the estimation of the response variable and updates Pareto-coordinates and the observation index for both new nodes.

Usage

estimEAT(data, leaves, t, xi, s, y)

Arguments

Value

Left and right children nodes.

Get EATBoost leaves supports

Description

Calculates the inferior corner of the leaves supports of a EATBoost model.

Usage

get.a.EATBoost(EATBoost_model)

Arguments

Value

data.frame with the leave supports

Get the inferior corner of the leave support from all trees of EATBoost

Description

Calculates the inferior corner of the support of all leave nodes of every tree created in the EATBoost model

Usage

get.a.trees(EATBoost_model)

Arguments

Value

list of matrix. The length of the list is equal to the num.iterations of the EATBoost_model. Each matrix corresponds to a tree, where the number of columns is the number of input variables and the number of rows to the number of leaves

Get the superior corner of the leave support from all trees of EATBoost

Description

Calculates the superior corner of the support of all leave nodes of every tree created in the EATBoost model

Usage

get.b.trees(EATBoost_model)

Arguments

Value

list of matrix. The length of the list is equal to the num.iterations of the EATBoost_model. Each matrix corresponds to a tree, where the number of columns is the number of input variables and the number of rows to the number of leaves

Get intersection between two leaves supports

Description

Calculates the intersection between two leave nodes from different trees of a EATBoost model.

Usage

get.intersection.a(comb_a_actual, comb_b_actual)

Arguments

Value

vector with the intersection. NULL if intersection is not valid.

Is Final Node

Description

This function evaluates a node and checks if it fulfills the conditions to be a final node.

Usage

isFinalNode(obs, data, numStop)

Arguments

Value

True if the node is a final node and false in any other case.

Mean Squared Error

Description

This function computes the mean squared error between two numeric vectors.

Usage

mse(y, yPred)

Arguments

Value

Mean Squared Error.

Mean Squared Error

Description

This function calculates the Mean Square Error between the predicted value and the observations in a given node.

Usage

mse_tree(data, t, y)

Arguments

Value

Mean Square Error at a node.

Position of the node

Description

This function finds the node where a register is located.

Usage

posIdNode(tree, idNode)

Arguments

Value

Position of the node or -1 if it is not found.

Data Pre-processing for Multivariate Adaptive Frontier Splines.

Description

This function arranges the data in the required format and displays error messages.

Usage

preProcess(data, x, y, na.rm = TRUE)

Arguments

Value

It returns a data.frame in the required format.

Model Prediction for DEA

Description

This function predicts the expected output by a DEA object.

Usage

## S3 method for class 'DEA'
predict(object, newdata, x, y, ...)

Arguments

Value

data.frame with the predicted values. Valid measures are: rad.out.

Model Prediction for Efficiency Analysis Trees.

Description

This function predicts the expected output by an EAT object.

Usage

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

Arguments

Value

data.frame with the predicted values.

Model prediction for EATBoost algorithm

Description

This function predicts the expected output by a EATBoost object.

Usage

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

Arguments

Value

data.frame with the predicted values.

Model Prediction for FDH

Description

This function predicts the expected output by a FDH object.

Usage

## S3 method for class 'FDH'
predict(object, newdata, x, y, ...)

Arguments

Value

data.frame with the predicted values. Valid measures are: rad.out.

Model Prediction for Adapted Multivariate Adaptive Frontier Splines.

Description

This function predicts the expected output by a MARS object.

Usage

## S3 method for class 'MARSAdapted'
predict(object, newdata, x, class = 1, ...)

Arguments

Value

data.frame with the predicted values.

Model Prediction for Boosted Multivariate Adaptive Frontier Splines

Description

This function predicts the expected output by a MARSBoost object.

Usage

## S3 method for class 'MARSBoost'
predict(object, newdata, x, class = 1, ...)

Arguments

Value

data.frame with the predicted values.

Efficiency Analysis Trees Predictor

Description

This function predicts the expected value based on a set of inputs.

Usage

predictor(tree, register)

Arguments

Value

The expected value of the dependent variable based on the given register.

Split node

Description

This function gets the variable and split value to be used in estimEAT, selects the best split and updates VarInfo, node indexes and leaves list.

Usage

split(data, tree, leaves, t, x, y, numStop)

Arguments

Value

Leaves and tree lists updated with the new child nodes.