Title:	Efficiency Analysis Trees
Version:	0.1.4
Description:	Functions are provided to determine production frontiers and technical efficiency measures through non-parametric techniques based upon regression trees. The package includes code for estimating radial input, output, directional and additive measures, plotting graphical representations of the scores and the production frontiers by means of trees, and determining rankings of importance of input variables in the analysis. Additionally, an adaptation of Random Forest by a set of individual Efficiency Analysis Trees for estimating technical efficiency is also included. More details in: <doi:10.1016/j.eswa.2020.113783>.
License:	GPL-3
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.2.1
Imports:	dplyr, conflicted, stats, ggplot2, ggparty, partykit, ggrepel, Rdpack, lpSolveAPI, utils, reshape2
Suggests:	rmarkdown, testthat, knitr, kableExtra, devtools
RdMacros:	Rdpack
VignetteBuilder:	knitr
Depends:	R (≥ 2.10)
URL:	https://efficiencytools.wordpress.com/
BugReports:	https://github.com/MiriamEsteve/EAT/issues
NeedsCompilation:	no
Packaged:	2023-01-10 08:53:37 UTC; Miriam_Esteve
Author:	Miriam Esteve [cre, aut], Víctor España [aut], Juan Aparicio [aut], Xavier Barber [aut]
Maintainer:	Miriam Esteve <mestevecampello@gmail.com>
Repository:	CRAN
Date/Publication:	2023-01-10 09:20:16 UTC

EAT: Efficiency Analysis Trees

Description

This package provides functions to determine production frontiers and technical efficiency measures through non-parametric techniques based upon regression trees. The package includes code for estimating radial input, output, directional and additive measures, plotting graphical representations of the scores and the production frontiers by means of trees, and determining rankings of importance of input variables in the analysis. Additionally, an adaptation of Random Forest by a set of individual Efficiency Analysis Trees for estimating technical efficiency is also included.

Author(s)

Mantainers:

• Miriam Esteve Campello mestevecampello@gmail.es

• Víctor Javier España Roch

Authors:

• Miriam Esteve Campello

• Víctor Javier España Roch

• Juan Aparicio Baeza

• Xavier Barber Vallés

See Also

Github: https://github.com/MiriamEsteve/EAT Esteve M, Aparicio J, Rabasa A, Rodriguez-Sala JJ (2020). “Efficiency analysis trees: A new methodology for estimating production frontiers through decision trees.” Expert Systems with Applications, 162, 113783.

Banker, Charnes and Cooper programming model with input orientation for a Convexified Efficiency Analysis Trees model

Description

Banker, Charnes and Cooper programming model with input orientation for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_BCC_in(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with scores.

Banker, Charnes and Cooper programming model with output orientation for a Convexified Efficiency Analysis Trees model

Description

Banker, Charnes and Cooper programming model with output orientation for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_BCC_out(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Directional Distance Function mathematical programming model for a Convexified Efficiency Analysis Trees model

Description

Directional Distance Function for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_DDF(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with scores.

Russell Model with input orientation for a Convexified Efficiency Analysis Trees model

Description

Russell Model with input orientation for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_RSL_in(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with scores.

Russell Model with output orientation for a Convexified Efficiency Analysis Trees model

Description

Russell Model with output orientation for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_RSL_out(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with scores.

Weighted Additive Model for a Convexified Efficiency Analysis Trees model

Description

Weighted Additive Model for a Convexified Efficiency Analysis Trees model.

Usage

CEAT_WAM(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves, weights)

Arguments

Value

A numerical vector with scores.

Efficiency Analysis Trees

Description

This function estimates a stepped production frontier through regression trees.

Usage

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

Arguments

Details

The EAT function generates a regression tree model based on CART (Breiman et al. 1984) 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 (Deprins and Simar 1984) but enhances some of its disadvantages such as the overfitting problem or the underestimation of technical inefficiency. More details in Esteve et al. (2020).

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.

References

Breiman L, Friedman J, Stone CJ, Olshen RA (1984). Classification and regression trees. CRC press.

Deprins D, Simar L (1984). “Measuring labor efficiency in post offices, The Performance of Public Enterprises: Concepts and Measurements, M. Marchand, P. Pestieau and H. Tulkens.”

Esteve M, Aparicio J, Rabasa A, Rodriguez-Sala JJ (2020). “Efficiency analysis trees: A new methodology for estimating production frontiers through decision trees.” Expert Systems with Applications, 162, 113783.

Examples

# ====================== #
# Single output scenario #
# ====================== #

simulated <- Y1.sim(N = 50, nX = 3)
EAT(data = simulated, x = c(1, 2, 3), y = 4, numStop = 10, fold = 5, max.leaves = 6)

# ====================== #
#  Multi output scenario #
# ====================== #

simulated <- X2Y2.sim(N = 50, border = 0.1)
EAT(data = simulated, x = c(1,2), y = c(3, 4), numStop = 10, fold = 7, max.depth = 7)

Banker, Charnes and Cooper Programming Model with Input Orientation for an Efficiency Analysis Trees model

Description

Banker, Charnes and Cooper programming model with input orientation for an Efficiency Analysis Trees model.

Usage

EAT_BCC_in(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Banker, Charnes and Cooper Programming Model with Output Orientation for an Efficiency Analysis Trees model

Description

Banker, Charnes and Cooper programming model with output orientation for an Efficiency Analysis Trees model.

Usage

EAT_BCC_out(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Directional Distance Function Programming Model for an Efficiency Analysis Trees model

Description

Directional Distance Function for an Efficiency Analysis Trees model.

Usage

EAT_DDF(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Russell Model with Input Orientation for an Efficiency Analysis Trees model

Description

Russell Model with input orientation for an Efficiency Analysis Trees model.

Usage

EAT_RSL_in(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Russell Model with Output Orientation for an Efficiency Analysis Trees model

Description

Russell Model with output orientation for an Efficiency Analysis Trees model.

Usage

EAT_RSL_out(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves)

Arguments

Value

A numerical vector with efficiency scores.

Weighted Additive Model for an Efficiency Analysis Trees model

Description

Weighted Additive Model for an Efficiency Analysis Trees model.

Usage

EAT_WAM(j, scores, x_k, y_k, atreeTk, ytreeTk, nX, nY, N_leaves, weights)

Arguments

Value

A numerical vector with efficiency scores.

Output Levels in an Efficiency Analysis Trees model

Description

This function returns the frontier output levels for an Efficiency Analysis Trees model.

Usage

EAT_frontier_levels(object)

Arguments

Value

A data.frame with the frontier output levels at the leaf nodes of the Efficiency Analysis Trees model introduced.

Examples

simulated <- Y1.sim(N = 50, nX = 3)
EAT_model <- EAT(data = simulated, x = c(1, 2, 3), y = 4, numStop = 10, fold = 5)
EAT_frontier_levels(EAT_model)

Descriptive Summary Statistics Table for the Leaf Nodes of an Efficiency Analysis Trees model

Description

This function returns a descriptive summary statistics table for each output variable calculated from the leaf nodes observations of an Efficiency Analysis Trees model. Specifically, it computes the number of observations, the proportion of observations, the mean, the variance, the standard deviation, the minimum, the first quartile, the median, the third quartile, the maximum and the root mean squared error.

Usage

EAT_leaf_stats(object)

Arguments

Value

A list or a data.frame (for 1 output scenario) with the following summary statistics:

• N: number of observations.

• Proportion: proportion of observations.

• mean: mean.

• var: variance.

• sd: standard deviation.

• min: minimun.

• Q1: first quartile.

• median: median.

• Q3: third quartile.

• max: maximum.

• RMSE: root mean squared error.

Examples

simulated <- Y1.sim(N = 50, nX = 3)
EAT_model <- EAT(data = simulated, x = c(1, 2, 3), y = 4, numStop = 10, fold = 5)
EAT_leaf_stats(EAT_model)

Create a EAT object

Description

This function saves information about the Efficiency Analysis Trees model.

Usage

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

Arguments

Value

An EAT object.

Number of Leaf Nodes in an Efficiency Analysis Trees model

Description

This function returns the number of leaf nodes for an Efficiency Analysis Trees model.

Usage

EAT_size(object)

Arguments

Value

Number of leaf nodes of the Efficiency Analysis Trees model introduced.

Examples

simulated <- Y1.sim(N = 50, nX = 3)
EAT_model <- EAT(data = simulated, x = c(1, 2, 3), y = 4, numStop = 10, fold = 5)
EAT_size(EAT_model)

Breiman Importance

Description

This function evaluates the importance of each predictor by the notion of surrogate splits.

Usage

M_Breiman(object, digits)

Arguments

Value

Dataframe with one column and the importance of each variable in rows.

PISA score and social index by country

Description

A dataset containing the PISA score in mathematics, reading and science and 13 variables related to the social index by country for 2018.

Usage

PISAindex

Format

A data frame with 72 rows and 18 variables:

Country

Country name

Continent

Country continent

S_PISA

PISA score in Science

R_PISA

PISA score in Reading

M_PISA

PISA score in Mathematics

NBMC

Nutritional and Basic Medical Care

WS

Water and Sanitation

S

Shelter

PS

Personal Safety

ABK

Access to Basic Knowledge

AIC

Access to Information and Communication

HW

Health and Wellness

EQ

Environmental Quality

PR

Personal Rights

PFC

Personal Freedom and Choice

I

Inclusiveness

AAE

Access to Advanced Education

GDP_PPP

Gross Domestic Product per capita adjusted by purchasing power parity

Source

https://www.socialprogress.org/

https://www.oecd.org/pisa/Combined_Executive_Summaries_PISA_2018.pdf

Branch Pruning

Description

This function computes the error of a branch as the sum of the errors of its child nodes.

Usage

RBranch(t, tree)

Arguments

Value

A list containing (1) the sum of the errors of the child nodes of the pruned node and (2) the total number of leaf nodes that come from it.

RCV

Description

RCV

Usage

RCV(N, Lv, y, alphaIprim, fold, TAiv)

Arguments

Value

Set of best pruning and the associated error calculated with test sets.

Random Forest + Efficiency Analysis Trees

Description

This function builds m individual Efficiency Analysis Trees in a forest structure.

Usage

RFEAT(data, x, y, numStop = 5, m = 50, s_mtry = "BRM", na.rm = TRUE)

Arguments

Value

A RFEAT 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

  • numStop: numStop hyperparameter value.

  • m: m hyperparameter value.

  • s_mtry: s_mtry hyperparameter value.

  • na.rm: na.rm hyperparameter value.

• forest: list containing the individual EAT models.

• error: Out-of-Bag error at the forest.

• OOB: list containing Out-of-Bag set for each tree.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.1)

RFmodel <- RFEAT(data = simulated, x = c(1,2), y = c(3, 4), numStop = 5,
                  m = 50, s_mtry = "BRM", na.rm = TRUE)

Create a RFEAT object

Description

This function saves information about the Random Forest for Efficiency Analysis Trees model.

Usage

RFEAT_object(
  data,
  x,
  y,
  rownames,
  numStop,
  m,
  s_mtry,
  na.rm,
  forest,
  error,
  OOB
)

Arguments

Value

A RFEAT object.

Random Forest + Efficiency Analysis Trees Predictor

Description

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

Usage

RF_predictor(forest, xn)

Arguments

Value

Vector of predictions.

Individual EAT for Random Forest

Description

This function builds an individual tree for Random Forest

Usage

RandomEAT(data, x, y, numStop, s_mtry)

Arguments

Value

A list of m trees in forest and the error that will be used in the ranking of the importance of the variables.

SERules

Description

Based on Validation tests over BestTivs, a new range of scores is obtained to find new pruned trees.

Usage

SERules(N, Lv, y, fold, Tk_score, BestTivs)

Arguments

Value

Value to get a range where new pruning is found.

2 Inputs & 2 Outputs Data Generation

Description

This function is used to simulate the data in a scenario with 2 inputs and 2 outputs.

Usage

X2Y2.sim(N, border, noise = NULL)

Arguments

Value

data.frame with simulated data.

Single Output Data Generation

Description

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

Usage

Y1.sim(N, nX)

Arguments

Value

data.frame with simulated data.

Alpha Calculation for Pruning Procedure of Efficiency Analysis Trees

Description

This function gets the minimum alpha for each subtree evaluated during the pruning procedure of the Efficiency Analysis Trees technique.

Usage

alpha(tree)

Arguments

Value

Numeric value corresponding to the minimum alpha associated with a suitable node to be pruned.

Bagging data

Description

Bootstrap aggregating for data.

Usage

bagging(data, x, y)

Arguments

Value

List containing training dataframe and list with binary response as 0 if the observations have been selected for training and 0 in any other case.

Barplot Variable Importance

Description

This function generates a barplot with the importance of each predictor.

Usage

barplot_importance(m, threshold)

Arguments

Value

Barplot representing each variable on the x-axis and its importance on the y-axis.

Tuning an Efficiency Analysis Trees model

Description

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

Usage

bestEAT(
  training,
  test,
  x,
  y,
  numStop = 5,
  fold = 5,
  max.depth = NULL,
  max.leaves = NULL,
  na.rm = TRUE
)

Arguments

Value

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

Examples

data("PISAindex")

n <- nrow(PISAindex) # Observations in the dataset
selected <- sample(1:n, n * 0.7) # Training indexes
training <- PISAindex[selected, ] # Training set
test <- PISAindex[- selected, ] # Test set

bestEAT(training = training, 
        test = test,
        x = 6:9,
        y = 3,
        numStop = c(3, 5, 7),
        fold = c(5, 7, 10))

Tuning a Random Forest + Efficiency Analysis Trees model

Description

This funcion computes the root mean squared error (RMSE) for a set of Random FOrest + Efficiency Analysis Trees models built with a grid of given hyperparameters.

Usage

bestRFEAT(
  training,
  test,
  x,
  y,
  numStop = 5,
  m = 50,
  s_mtry = c("5", "BRM"),
  na.rm = TRUE
)

Arguments

Value

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

Examples

data("PISAindex")

n <- nrow(PISAindex) # Observations in the dataset
selected <- sample(1:n, n * 0.7) # Training indexes
training <- PISAindex[selected, ] # Training set
test <- PISAindex[- selected, ] # Test set

bestRFEAT(training = training, 
          test = test,
          x = 6:9,
          y = 3,
          numStop = c(3, 5),
          m = c(20, 30),
          s_mtry = c("1", "BRM"))

Check Efficiency Analysis Trees.

Description

This function verifies if a specific tree keeps to Pareto-dominance properties.

Usage

checkEAT(tree)

Arguments

Value

Message indicating if the tree is acceptable or warning in case of breaking any Pareto-dominance relationship.

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.depth = NULL, max.leaves = NULL)

Arguments

Value

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

Efficiency Scores computed through a Convexified Efficiency Analysis Trees model.

Description

This function computes the efficiency scores for each DMU through a Convexified Efficiency Analysis Trees model.

Usage

efficiencyCEAT(
  data,
  x,
  y,
  object,
  scores_model,
  digits = 3,
  DEA = TRUE,
  print.table = FALSE,
  na.rm = TRUE
)

Arguments

Value

A data.frame with the efficiency scores computed through a Convexified Efficiency Analysis Trees model. Optionally, a summary descriptive table of the efficiency scores can be displayed.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

efficiencyCEAT(data = simulated, x = c(1, 2), y = c(3, 4), object = EAT_model, 
              scores_model = "BCC.OUT", digits = 2, DEA = TRUE, print.table = TRUE,
              na.rm = TRUE)

Efficiency Scores Density Plot

Description

Density plot for efficiency scores.

Usage

efficiencyDensity(df_scores, model = c("EAT", "FDH"))

Arguments

Value

Density plot for efficiency scores.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)

EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

scores <- efficiencyEAT(data = simulated, x = c(1, 2), y = c(3, 4), object = EAT_model, 
                        scores_model = "BCC.OUT", digits = 2, FDH = TRUE, na.rm = TRUE)
                        
efficiencyDensity(df_scores = scores,
                  model = c("EAT", "FDH"))
 

Efficiency Scores computed through an Efficiency Analysis Trees model.

Description

This function computes the efficiency scores for each DMU through an Efficiency Analysis Trees model.

Usage

efficiencyEAT(
  data,
  x,
  y,
  object,
  scores_model,
  digits = 3,
  FDH = TRUE,
  print.table = FALSE,
  na.rm = TRUE
)

Arguments

Value

A data.frame with the efficiency scores computed through an Efficiency Analysis Trees model. Optionally, a summary descriptive table of the efficiency scores can be displayed.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

efficiencyEAT(data = simulated, x = c(1, 2), y = c(3, 4), object = EAT_model, 
              scores_model = "BCC.OUT", digits = 2, FDH = TRUE, print.table = TRUE,
              na.rm = TRUE)

Efficiency Scores Jitter Plot

Description

This function returns a jitter plot from ggplot2. This graphic shows how DMUs are grouped into leaf nodes in a model built using the EAT function. Each leaf node groups DMUs with the same level of resources. The dot and the black line represent, respectively, the mean value and the standard deviation of the scores of its node. Additionally, efficient DMU labels always are displayed based on the model entered in the scores_model argument. Finally, the user can specify an upper bound upn and a lower bound lwb in order to show, in addition, the labels whose efficiency score lies between them.

Usage

efficiencyJitter(object, df_scores, scores_model, upb = NULL, lwb = NULL)

Arguments

Value

Jitter plot with DMUs and scores.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

EAT_scores <- efficiencyEAT(data = simulated, x = c(1, 2), y = c(3, 4), object = EAT_model,
                            scores_model = "BCC.OUT", digits = 2, na.rm = TRUE)

efficiencyJitter(object = EAT_model, df_scores = EAT_scores, scores_model = "BCC.OUT")

Efficiency Scores computed through a Random Forest + Efficiency Analysis Trees model.

Description

This function computes the efficiency scores for each DMU through a Random Forest + Efficiency Analysis Trees model and the Banker Charnes and Cooper mathematical programming model with output orientation. Efficiency level at 1.

Usage

efficiencyRFEAT(
  data,
  x,
  y,
  object,
  digits = 3,
  FDH = TRUE,
  print.table = FALSE,
  na.rm = TRUE
)

Arguments

Value

A data.frame with the efficiency scores computed through a Random Forest + Efficiency Analysis Trees model. Optionally, a summary descriptive table of the efficiency scores can be displayed.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
RFEAT_model <- RFEAT(data = simulated, x = c(1,2), y = c(3, 4))

efficiencyRFEAT(data = simulated, x = c(1, 2), y = c(3, 4), object = RFEAT_model, 
                digits = 2, FDH = TRUE, na.rm = TRUE)

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.

Efficiency Analysis Trees Frontier Graph

Description

This function displays a plot with the frontier estimated by Efficiency Analysis Trees in a scenario of one input and one output.

Usage

frontier(
  object,
  FDH = FALSE,
  observed.data = FALSE,
  observed.color = "black",
  pch = 19,
  size = 1,
  rwn = FALSE,
  max.overlaps = 10
)

Arguments

Value

Plot with estimated production frontier

Examples

simulated <- Y1.sim(N = 50, nX = 1)

model <- EAT(data = simulated,
             x = 1,
             y = 2)

frontier <- frontier(object = model,
                     FDH = TRUE, 
                     observed.data = TRUE,
                     rwn = TRUE)
plot(frontier)

Train and Test Sets Generation

Description

This function splits the original data in two new data sets: a train set and a test set.

Usage

generateLv(data, fold)

Arguments

Value

A list structure with the train and the test set.

Breiman's Variable Importance

Description

This function recalculates all the possible splits, with the exception of the one being used, and for each node and variable gets the best split based on their degree of importance.

Usage

imp_var_EAT(data, tree, x, y, digits)

Arguments

Value

A dataframe with the best split for each node and its variable importance.

Variable Importance through Random Forest + Efficiency Analysis Trees

Description

Variable Importance through Random Forest + Efficiency Analysis Trees.

Usage

imp_var_RFEAT(object, digits = 2)

Arguments

Value

Vector of input importance scores

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.

Layout for nodes in plotEAT

Description

This function modifies the coordinates of the nodes in the plotEAT function to overcome overlapping.

Usage

layout(py)

Arguments

Value

Dataframe with suitable modifications of the node layout.

Mean Squared Error

Description

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

Usage

mse(data, t, y)

Arguments

Value

Mean Square Error at a node.

Random Selection of Variables

Description

This function randomly selects the variables that are evaluated to divide a node and removes those that do not present variability.

Usage

mtry_inputSelection(data, x, t, mtry)

Arguments

Value

Index of the variables by which the node is divided.

Efficiency Analysis Trees Plot

Description

Plot a tree-structure for an Efficiency Analysis Trees model.

Usage

plotEAT(object)

Arguments

Value

Plot object with the following elements for each node:

• id: node index.

• R: error at the node.

• n(t): number of observations at the node.

• an input name: splitting variable.

• y: output prediction.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

plotEAT(EAT_model)

Random Forest + Efficiency Analysis Trees Plot

Description

Plot a graph with the Out-of-Bag error for a forest consisting of m trees.

Usage

plotRFEAT(object)

Arguments

Value

Line plot with the OOB error and the number of trees in the forest.

Examples

simulated <- Y1.sim(N = 150, nX = 6)
RFmodel <- RFEAT(data = simulated, x = 1:6, y = 7, numStop = 10,
                  m = 50, s_mtry = "BRM", na.rm = TRUE)
plotRFEAT(RFmodel)

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 Preprocessing for Efficiency Analysis Trees

Description

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

Usage

preProcess(
  data,
  x,
  y,
  numStop = 5,
  fold = 5,
  max.depth = NULL,
  max.leaves = NULL,
  na.rm = TRUE
)

Arguments

Value

It returns a data.frame in the required format.

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 original data and the predicted values.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

predict(object = EAT_model, newdata = simulated, x = c(1, 2))

Model prediction for Random Forest + Efficiency Analysis Trees model.

Description

This function predicts the expected output by a RFEAT object.

Usage

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

Arguments

Value

data.frame with the original data and the predicted values.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
RFEAT_model <- RFEAT(data = simulated, x = c(1, 2), y = c(3, 4))

predict(object = RFEAT_model, newdata = simulated, x = c(1, 2))

Model prediction for Free Disposal Hull

Description

This function predicts the expected output by a Free Disposal Hull model.

Usage

predictFDH(data, x, y)

Arguments

Value

Data frame with the original data and the predicted values through a Free Disposal Hull model.

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.

Ranking of Variables by Efficiency Analysis Trees model.

Description

This function computes the variable importance through an Efficiency Analysis Trees model.

Usage

rankingEAT(object, barplot = TRUE, threshold = 70, digits = 2)

Arguments

Value

data.frame with the importance scores and a barplot representing the the variable importance if barplot = TRUE.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
EAT_model <- EAT(data = simulated, x = c(1,2), y = c(3, 4))

rankingEAT(object = EAT_model,
           barplot = TRUE,
           threshold = 70,
           digits = 2)

Ranking of variables by Random Forest + Efficiency Analysis Trees model.

Description

This function calculates variable importance through a Random Forest + Efficiency Analysis Trees model.

Usage

rankingRFEAT(object, barplot = TRUE, digits = 2)

Arguments

Value

data.frame with the importance scores and a barplot representing the variable importance if barplot = TRUE.

Examples

simulated <- X2Y2.sim(N = 50, border = 0.2)
RFEAT_model <- RFEAT(data = simulated, x = c(1,2), y = c(3, 4))

rankingRFEAT(object = RFEAT_model,
             barplot = TRUE,
             digits = 2)

Pruning Scores

Description

This function calculates the score for each pruning of tree_alpha_list.

Usage

scores(N, Lv_notLv, x, y, fold, numStop, Tk, tree_alpha_list)

Arguments

Value

List with the best pruning for each fold, the pruning with a lower score and tree_alpha_list with scores updated.

Select Tk

Description

This function tries to find a new pruned tree with a shorter length and a score in the range generated for SE.

Usage

selectTk(Tk, tree_alpha_list, SE)

Arguments

Value

The same best tree or a new suitable one.

Select Possible Inputs in Split.

Description

This function selects the number of inputs for a split in Random Forest.

Usage

select_mtry(s_mtry, t, nX, nY)

Arguments

Value

Number of inputs selected according to the specified rule.

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.

Split Node in Random Forest EAT

Description

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

Usage

split_forest(data, tree, leaves, t, x, y, numStop, arrayK)

Arguments

Value

Leaves and tree lists updated with the new child nodes.

Trees for RCV

Description

This function generates a deep EAT and all pruning for each train set.

Usage

treesForRCV(notLv, x, y, fold, numStop)

Arguments

Value

List with each possible pruning for the deep tree generated with train set and its associated alpha values.