adea (version 1.5.1)

adea: ADEA analysis to variable selection in DEA

Description

It does an ADEA analysis. In particular it computes a score for each DMU and a load for each variable.

Usage

adea(
  input,
  output,
  orientation = c("input", "output"),
  load.orientation = c("inoutput", "input", "output"),
  name = "",
  solver = "auto"
)

Value

The function returns an adea class object with the following named members:

• name: A label of the model

• orientation: DEA model orientation 'input' or 'output'

• load.orientation: load DEA model orientation 'input', 'output', or 'inoutput'

• inputnames: Variable input names

• outputnames: Variable output names

• eff: is a vector with DMU's scores

• loads: A list with all information about loads:

  • load: The lowest load, which is the load of the ADEA model

  • input: A vector with loads of input variables

  • iinput: Index of input variable that reach the load of the model

  • output: A vector with loads of output variables

  • ioutput: Index of output variable that reach the load of the model

• ux: A set of weights for inputs

• vy: A set of weights for output

• vinput: Standardized virtual input dividing by the sum of the weights, see [Costa2006] in adea-package.

• voutput: Standardized virtual output dividing by the sum of the weights, see [Costa2006] in adea-package

• solver: The solver used for the resolution of the optimization problem

Arguments

input

A matrix or a data frame containing the inputs of the units to be evaluated, with one row for each DMU and one column for each input.

output

A matrix or a data frame containing the outputs of the units to be evaluated, with one row for each DMU and one column for each output.

orientation

Use "input" for input orientation or "output" for output orientation in DEA model. The default is "input".

load.orientation

This parameter allows the selection of variables to be included in load analysis. The default is "inoutput" which means that all input and output variables will be included. Use "input" or "output" to include only input or output variables in load analysis.

name

An optional descriptive name for the model. The default is an empty string. This name will be displayed in printed and summarized results.

solver

The solver used by ROI to solve the DEA optimization problem. The default is "auto." The solver must be installed and capable of solving linear programming problems. Use ROI_installed_solvers() to list them.

Details

The selection of input and output variables for inclusion in a DEA model is a critical aspect, as many studies have revealed. adea function provides an implementation of the ADEA method for variable selection in DEA.

ADEA methodology introduces a new phase in classical DEA analysis, measuring the relative importance of each input and output variable. This measure is referred to as load or contribution. It also defines a load for the entire model. Using this measure, a procedure has been developed to select an optimised or relevant set of variables.

A variable's load is a standardized ratio of the efficiency scores of all DMUs due to that variable. These loads quantify the contribution of each variable to the overall model. Where 0 means that the contribution of that variable to the efficiency values is negligible. The ideal load is 1, and values range from 0 to the number of input or output variables. The lowest load value has a real significance as it represents the variable with the least contribution to efficiency.

As it is usually done in DEA, these loads are computed as its maximum allowable value using alternative sets of weights but without changing the efficiency scores. But because the sum of all of them is fixed, when one variable increases its load, any other decrease in value. So only the lowest value of all loads has a real meaning. This lowest value can be taken as a significance measure of the entire model.

This measure, load, has two key properties that easy its interpretation:

• It has a bounded range from 0 to the number of input or output variables, with 1 as the ideal value.

• It is invariant by changes in scale.

ADEA analysis can be done considering only input variables, in this case ADEA analysis has input as load.orientation value. output when only output variables are considered. And inoutput load.orientation when all variables in the model are taken into account.

Adea models, as the DEA models, can be input or output orientated. Input orientated DEA models propose to reach the efficiency of DMUs through a reduction in the amount of input required by non efficient DMUs. On the contrary, output orientated DEA models propose to increase the amount of output of non efficient DMUs.

For a detailed description of the maths behind the model, see the references.

References

Stepwise Selection of Variables in DEA Using Contribution Load. F. Fernandez-Palacin, M. A. Lopez-Sanchez and M. Munoz-Marquez. Pesquisa Operacional 38 (1), pg. 1-24, 2018. <DOI:10.1590/0101-7438.2018.038.01.0000>.

Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis. Jeyms Villanueva-Cantillo and Manuel Munoz-Marquez. European Journal of Operational Research, 290 (2), pg. 657-670, 2021. <DOI:10.1016/j.ejor.2020.08.021>. #

See Also

adea-package.

Examples

# Load data
data('cardealers4')

# Define input and output
input <- cardealers4[, c('Employees', 'Depreciation')]
output <- cardealers4[, c('CarsSold', 'WorkOrders')]

# Compute adea model
model <- adea(input, output, name = 'ADEA for cardealers4 dataset')
model
# Dealer A  Dealer B  Dealer C  Dealer D  Dealer E  Dealer F
# 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044

# Get model's load
model$loads$load
# [1] 0.6666667

# Get variable loads
model$loads
# $load
# [1] 0.6666667
# $input
# Employees Depreciation
# 0.6666667    1.3333333
# $iinput
# Employees 
#         1 
# $output
# CarsSold WorkOrders
# 1.2663476  0.7336524 
# $ioutput
# WorkOrders 
#          2 

# Summarize the model and print additional information
summary(model)
# Model name              ADEA for cardealers4 dataset
# Orientation                                    input
# Load orientation                            inoutput
# Model load                         0.666666666666659
# Input load.Employees               0.666666666666659
# Input load.Depreciation             1.33333333333334
# Output load.CarsSold                 1.1025075271907
# Output load.WorkOrders               0.8974924728093
# Inputs                        Employees Depreciation
# Outputs                          CarsSold WorkOrders
# nInputs                                            2
# nOutputs                                           2
# nVariables                                         4
# nEfficients                                        2
# Eff. Mean                           0.90022318389575
# Eff. sd                            0.135194867030839
# Eff. Min.                          0.651504424778761
# Eff. 1st Qu.                       0.872252747252747
# Eff. Median                        0.942225031605562
# Eff. 3rd Qu.                       0.997898230088495
# Eff. Max.                                          1