In MiriamEsteve/EAT: Efficiency Analysis Trees

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eat

The EAT algorithm performs a regression tree based on CART methodology under a new approach that guarantees obtaining a frontier as estimator that fulfills the property of free disposability. This new technique has been baptized as Efficiency Analysis Trees. Some of its main functions are:

To create homogeneous groups of DMUs in terms of their inputs and to know for each of these groups, what is the maximum expected output.
To know which DMUs exercise best practices and which of them do not obtain a performance according to their resources level.
To know what variables are more relevant in obtaining efficient levels of output.

Installation

You can install the released version of eat from CRAN with:

install.packages("eat")

And the development version from GitHub with:

devtools::install_github("MiriamEsteve/EAT")

Example

library(eat)
data("PISAindex")

EAT model with 1 input (NBMC) and 1 output (S_PISA)

single_model <- EAT(data = PISAindex, 
                    x = 15, # input 
                    y = 3) # output

Print an EAT object

print(single_model)

Summary of an EAT object

summary(single_model)

Number of leaf nodes of an EAT object

EAT_size(single_model)

Frontier levels of output for an EAT object

EAT_frontier_levels(single_model)

Descriptive analysis for an EAT object

EAT_leaf_stats(single_model)

Plot the frontier

frontier(object = single_model,
         FDH = TRUE, 
         observed.data = TRUE,
         rwn = TRUE)

EAT model with 13 inputs and 3 outputs

multioutput <- EAT(data = PISAindex, 
                   x = 6:18,
                   y = 3:5)

Ranking of importance of variables for EAT

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

Plot an EAT model

plotEAT(object = multioutput)

Tuning an EAT model

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

bestEAT(training = training, 
        test = test,
        x = 6:18,
        y = 3:5,
        numStop = c(5, 7, 10),
        fold = c(5, 7))

Efficiency scores EAT

single_model <- EAT(data = PISAindex, x = 15, y = 3)

scores_EAT <-  efficiencyEAT(data = PISAindex,
                            x = 15, 
                            y = 3,
                            object = single_model, 
                            scores_model = "BCC.OUT",
                            digits = 3,
                            FDH = TRUE,
                            print.table = TRUE)

Efficiency scores CEAT

scores_CEAT <- efficiencyCEAT(data = PISAindex,
                              x = 15, 
                              y = 3,
                              object = single_model, 
                              scores_model = "BCC.INP",
                              digits = 3,
                              DEA = TRUE,
                              print.table = TRUE)

Efficiency jitter plot

efficiencyJitter(object = single_model,
                 df_scores = scores_EAT$EAT_BCC_OUT,
                 scores_model = "BCC.OUT",
                 lwb = 1.2)

Efficiency density plot

efficiencyDensity(df_scores = scores_EAT[, 3:4],
                  model = c("EAT", "FDH"))

RFEAT model

forest <- RFEAT(data = PISAindex, 
                x = 6:18, 
                y = 5, 
                numStop = 5, 
                m = 30,
                s_mtry = "BRM",
                na.rm = TRUE)

Print a RFEAT object

print(forest)

Plot the Out-of-Bag error for a forest made up of k trees

plotRFEAT(forest)

RFEAT ranking

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

Tuning a RFEAT model

bestRFEAT(training = training, 
          test = test,
          x = 6:18,
          y = 3:5,
          numStop = c(5, 10),
          m = c(30, 40),
          s_mtry = c("BRM", "3"))

RFEAT scores

efficiencyRFEAT(data = PISAindex,
                x = 6:18,
                y = 5,
                object = forest,
                FDH = TRUE,
                print.table = TRUE)

EAT and RFEAT predictions

input <- c(6, 7, 8, 12, 17)
output <- 3:5

EAT_model <- EAT(data = PISAindex, x = input, y = output)
RFEAT_model <- RFEAT(data = PISAindex, x = input, y = output)

# PREDICTIONS
predictions_EAT <- predict(object = EAT_model, newdata = PISAindex[, input])
predictions_RFEAT <- predict(object = RFEAT_model, newdata = PISAindex[, input])