, Manuel Munoz-Marquez
[aut, cre] | Title: | Alternate DEA Package |
|---|---|
| Description: | The meaning of adea is "alternate DEA". This package is devoted to provide the alternative method of DEA described in the paper entitled "Stepwise Selection of Variables in DEA Using Contribution Load", by F. Fernandez-Palacin, M. A. Lopez-Sanchez and M. Munoz-Marquez. Pesquisa Operacional 38 (1), pg. 1-24, 2018. <doi:10.1590/0101-7438.2018.038.01.0031>. A full functional on-line and interactive version is available at <https://knuth.uca.es/shiny/DEA/>. |
| Authors: | Fernando Fernandez-Palacin [aut]
, Manuel Munoz-Marquez
[aut, cre] |
| Maintainer: | Manuel Munoz-Marquez <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.5.2 |
| Built: | 2024-11-13 03:36:49 UTC |
| Source: | https://github.com/cran/adea |
Package: adea Version: 1.5.2 Date: 2024-11-06 License: GPL (>= 3)
Data Envelopment Analysis (DEA) involves evaluating the efficiency of a set of Decision Making Units (DMUs) and calculating a relative efficiency score for each DMU. These scores are determined as a weighted ratio between all inputs and outputs amounts for such DMU.
DEA methodology assumes that all DMUs use the same set of inputs to produce the same set of outputs.
The selection of input and output variables for inclusion in a DEA model is a crucial aspect, as numerous studies have shown.
This package offers two variable selection procedures.
The first is ADEA, which is based on a measure of the relative importance of variables in the entire set of scores.
For more information on this methodology, see adea.
An alternative way to select the variables for the model is by solving a mathematical optimization problem that determines the optimal selection based on some performance criteria.
fsdea function provides an implementation of this procedure.
The main functions provided by this package are:
adea: Conducts ADEA analysis, providing efficiency scores for each DMU, a set of weights, and loads for each input and output variable, along with a model load.
adea_parametric: Does a stepwise analysis of removing variables step by steps. adea_hierarchical works in similar way.
fsea: Selects an optimal subset of input and output variables based on some performance criteria.
cadea: Performs Constrained ADEA analysis to enforce variable load constraints within a specified range, resulting in changes to efficiency scores.
adea_load_average: Identifies DMUs with a higher impact on the ADEA model.
This package is translation-ready, and contributions of translated versions of po files are highly welcome.
Fernando Fernandez-Palacin <[email protected]> and Manuel Munoz-Marquez <[email protected]>
Mantainer: Manuel Munoz-Marquez <[email protected]>
A new approach to the bi-dimensional representation of the DEA efficient frontier with multiple inputs and outputs. Carlos A. Bana e Costa and Joao Carlos C. B. Soares de Mello, and Lidia Angulo Meza. European Journal of Operational Research, 255 (1), pg. 175-186, 2016, <DOI:10.1016/j.ejor.2016.05.012>.
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>.
Feature Selection in Data Envelopment Analysis: A Mathematical Optimization approach. Benitez-Pena, S., Bogetoft, P., and Romero Morales, D.. Omega, Elsevier BV, 96, pp. 102068, 2020. <DOI:10.1016/j.omega.2019.05.004>
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>.
It does an ADEA analysis. In particular it computes a score for each DMU and a load for each variable.
adea( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", solver = "auto" )adea( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", solver = "auto" )
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 |
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.
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
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>. #
# 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 # $ioutput # WorkOrders # 2 # Summarize the model and print additional information summary(model) # Model name ADEA for cardealers4 dataset # Orientation input # Load orientation inoutput # Model load 0.666666666666659 # Input load.Employees 0.666666666666659 # Input load.Depreciation 1.33333333333334 # Output load.CarsSold 1.1025075271907 # Output load.WorkOrders 0.8974924728093 # Inputs Employees Depreciation # Outputs CarsSold WorkOrders # nInputs 2 # nOutputs 2 # nVariables 4 # nEfficients 2 # Eff. Mean 0.90022318389575 # Eff. sd 0.135194867030839 # Eff. Min. 0.651504424778761 # Eff. 1st Qu. 0.872252747252747 # Eff. Median 0.942225031605562 # Eff. 3rd Qu. 0.997898230088495 # Eff. Max. 1# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute adea model model <- adea(input, output, name = 'ADEA for cardealers4 dataset') model # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Get model's load model$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
This function returns a list of DEA models by systematically eliminating one variable at a time, following ADEA methodology.
adea_hierarchical( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), solver = "auto", verbose = 0 )adea_hierarchical( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), solver = "auto", verbose = 0 )
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. |
direction |
The direction in which the variables enter or exit the model. Currently, only the "backward" option is implemented. |
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 |
verbose |
Use 0 for minimal output, displaying only the final model. Use 1 or higher values to get detailed information for each step. The default is 0. This option affects only the printed output and not the result. |
This procedure provides a list of all DEA models for all nested sets of variables. In each model, the variable with lowest load is dropped. It's important to note that the load of the new model can be lower than that of the previous one. For more details, please refer to the examples section.
The function returns an object of the adeaparametric class 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').
loads: Load of each model.
models: List of all adea models.
ninputs: Number of input variables in each model.
noutputs: Number of output variables in each model.
nvariables: Number of variables in each model.
inputnames: Names of input variables in each model.
outputnames: Names of output variables in each model.
out: Variable dropped at each step.
solver: The solver used for resolving the optimization problem.
# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute all dea models in hierarchical manner sol.ah <- adea_hierarchical(input, output) # Print the result sol.ah # Loads nEfficients nVariables nInputs nOutputs Inputs Outputs # 4 0.6666667 2 4 2 2 Employees, Depreciation CarsSold, WorkOrders # 3 0.9575672 2 3 1 2 Depreciation CarsSold, WorkOrders # 2 1.0000000 1 2 1 1 Depreciation CarsSold # Summary the model with 3 variables summary(sol.ah$models[[3]]) # Model name # Orientation input # Load orientation inoutput # Model load 0.957567163474156 # Input load.Depreciation 1 # Output load.CarsSold 1.04243283652584 # Output load.WorkOrders 0.957567163474156 # Inputs Depreciation # Outputs CarsSold WorkOrders # nInputs 1 # nOutputs 2 # nVariables 3 # nEfficients 2 # Eff. Mean 0.90022318389575 # Eff. sd 0.135194867030839 # Eff. Min. 0.651504424778761 # Eff. 1st Qu. 0.872252747252747 # Eff. Median 0.942225031605563 # Eff. 3rd Qu. 0.997898230088496 # Eff. Max. 1 # Get efficiencies for the model with 3 variables sol.ah$models[[3]]$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute all dea models in hierarchical manner sol.ah <- adea_hierarchical(input, output) # Print the result sol.ah # Loads nEfficients nVariables nInputs nOutputs Inputs Outputs # 4 0.6666667 2 4 2 2 Employees, Depreciation CarsSold, WorkOrders # 3 0.9575672 2 3 1 2 Depreciation CarsSold, WorkOrders # 2 1.0000000 1 2 1 1 Depreciation CarsSold # Summary the model with 3 variables summary(sol.ah$models[[3]]) # Model name # Orientation input # Load orientation inoutput # Model load 0.957567163474156 # Input load.Depreciation 1 # Output load.CarsSold 1.04243283652584 # Output load.WorkOrders 0.957567163474156 # Inputs Depreciation # Outputs CarsSold WorkOrders # nInputs 1 # nOutputs 2 # nVariables 3 # nEfficients 2 # Eff. Mean 0.90022318389575 # Eff. sd 0.135194867030839 # Eff. Min. 0.651504424778761 # Eff. 1st Qu. 0.872252747252747 # Eff. Median 0.942225031605563 # Eff. 3rd Qu. 0.997898230088496 # Eff. Max. 1 # Get efficiencies for the model with 3 variables sol.ah$models[[3]]$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044
Search for leverage units (DMU's) with a greater impact on load levels in DEA analysis.
adea_load_leverage( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), load.diff = 0.05, ndel = 1, nmax = 0, solver = "auto" )adea_load_leverage( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), load.diff = 0.05, ndel = 1, nmax = 0, solver = "auto" )
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. |
load.diff |
Minimum difference in load to consider a subset of DMUs as a leverage one |
ndel |
Maximum number of units to drop out in each try. |
nmax |
Maximum number of DMU sets to include in results. 0 for no limit. |
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 |
A leverage unit is a DMU that significantly alters the results of the current procedure, in this case, a DMU that produce a large change in variable loads.
The function returns a list with the following named members:
loads: Load of each model after removing the corresponding DMUs
loads.diff: For each model the difference between its load and the original one
dmu.indexs: Index of DMUs removed in each model
This function has to solve a large number of large linear programs that grows with DMUs. So computation time required may be very large, be patient.
data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] adea_load_leverage(input, output, ndel = 2) # load load.diff DMUs # 1 1.0000000 0.33333333 1, 6 # 2 1.0000000 0.33333333 3, 4 # 3 1.0000000 0.33333333 2, 3 # 4 1.0000000 0.33333333 2, 5 # 5 1.0000000 0.33333333 4, 6 # 6 1.0000000 0.33333333 2 # 7 1.0000000 0.33333333 1, 4 # 8 1.0000000 0.33333333 2, 6 # 9 1.0000000 0.33333333 1, 2 # 10 0.9635628 0.29689609 2, 4 # 11 0.8743243 0.20765766 5, 6 # 12 0.8479940 0.18132736 1, 3 # 13 0.8420551 0.17538843 3, 6 # 14 0.8243243 0.15765766 1, 5 # 15 0.8000000 0.13333333 6 # 16 0.8000000 0.13333333 4 # 17 0.8000000 0.13333333 1 # 18 0.8000000 0.13333333 3 # 19 0.7461771 0.07951041 3, 5 # 20 0.7358231 0.06915643 5data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] adea_load_leverage(input, output, ndel = 2) # load load.diff DMUs # 1 1.0000000 0.33333333 1, 6 # 2 1.0000000 0.33333333 3, 4 # 3 1.0000000 0.33333333 2, 3 # 4 1.0000000 0.33333333 2, 5 # 5 1.0000000 0.33333333 4, 6 # 6 1.0000000 0.33333333 2 # 7 1.0000000 0.33333333 1, 4 # 8 1.0000000 0.33333333 2, 6 # 9 1.0000000 0.33333333 1, 2 # 10 0.9635628 0.29689609 2, 4 # 11 0.8743243 0.20765766 5, 6 # 12 0.8479940 0.18132736 1, 3 # 13 0.8420551 0.17538843 3, 6 # 14 0.8243243 0.15765766 1, 5 # 15 0.8000000 0.13333333 6 # 16 0.8000000 0.13333333 4 # 17 0.8000000 0.13333333 1 # 18 0.8000000 0.13333333 3 # 19 0.7461771 0.07951041 3, 5 # 20 0.7358231 0.06915643 5
The adea_loads function calculates variable loads for Data Envelopment Analysis (DEA) with user-specified weights for input and output variables.
adea_loads( input, output, ux, vy, load.orientation = c("inoutput", "input", "output") )adea_loads( input, output, ux, vy, load.orientation = c("inoutput", "input", "output") )
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. |
ux |
A matrix of weights for DMUs and input variables. |
vy |
A matrix of weights for DMUs and output variables. |
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. |
In DEA analysis, even when the efficiency scores remain constants, there is a significant degree of freedom in selecting the sets of weights for input and output variables.
Not all sets of weights assign the same importance to the variables. This function allows you to compute the load of each variable based on the provided weights. It also computes load.levels, which represents the minimum values of such loads.
It's important to note that different sets of weights result in different ways to model efficiency. This function does not solve any model. It provides the loads for the specified weights, as described in the theoretical ADEA model.
This function is primarily intended for research and internal use.
Loads for model, input and output variables
# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Make dea analysis model <- dea(input, output) # Show results 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 # Compute loads for such weights adea_loads(input, output, model$ux, model$vy) # $load # [1] 0 # $input # Employees Depreciation # 0 2 # $iinput # Employees # 1 # $output # CarsSold WorkOrders # 1.1025075 0.8974925 # $ioutput # WorkOrders# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Make dea analysis model <- dea(input, output) # Show results model # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Compute loads for such weights adea_loads(input, output, model$ux, model$vy) # $load # [1] 0 # $input # Employees Depreciation # 0 2 # $iinput # Employees # 1 # $output # CarsSold WorkOrders # 1.1025075 0.8974925 # $ioutput # WorkOrders
The function returns a list of DEA models, progressively removing at least one variable at each step. This process results in a sequence of models with increasing values ADEA loads.
adea_parametric( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), solver = "auto", verbose = 0 )adea_parametric( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), solver = "auto", verbose = 0 )
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. |
direction |
The direction in which the variables enter or exit the model. Currently, only the "backward" option is implemented. |
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 |
verbose |
Use 0 for minimal output, displaying only the final model. Use 1 or higher values to get detailed information for each step. The default is 0. This option affects only the printed output and not the result. |
The models are sorted by increasing values of loads, starting from initially given model and progressing to the one with one input and one output variable. Note that the load value for the model with one input and one output is 1. In each step, at least one variable is dropped, but more than one can be dropped if necessary.
See example for more details.
The function returns an adeaparametric 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').
loads: Load of each model.
models: List of all ADEA models.
ninputs: Number of input variables in each model.
noutputs: Number of output variables in each model.
nvariables: Number of variables in each model.
inputnames: Names of input variables in each model.
outputnames: Names of output variables in each model.
out: Variable, or variables, dropped in each step.
solver: The solver used for the resolution of the optimization problem.
# Read data data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute all dea models in parametric way and store in sol.ap sol.ap <- adea_parametric(input, output) # Show result sol.ap # Loads nEfficients nVariables nInputs nOutputs Inputs Outputs # 4 0.6666667 2 4 2 2 Employees, Depreciation CarsSold, WorkOrders # 3 0.9575672 2 3 1 2 Depreciation CarsSold, WorkOrders # 2 1.0000000 1 2 1 1 Depreciation CarsSold # Summary the model with 3 variables summary(sol.ap$models[[3]]) # Model name # Orientation input # Load orientation inoutput # Model load 0.957567163474156 # Input load.Depreciation 1 # Output load.CarsSold 1.04243283652584 # Output load.WorkOrders 0.957567163474156 # Inputs Depreciation # Outputs CarsSold WorkOrders # nInputs 1 # nOutputs 2 # nVariables 3 # nEfficients 2 # Eff. Mean 0.90022318389575 # Eff. sd 0.135194867030839 # Eff. Min. 0.651504424778761 # Eff. 1st Qu. 0.872252747252747 # Eff. Median 0.942225031605563 # Eff. 3rd Qu. 0.997898230088496 # Eff. Max. 1 # Get efficiencies for the model with 3 variables sol.ap$models[[3]]$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044# Read data data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute all dea models in parametric way and store in sol.ap sol.ap <- adea_parametric(input, output) # Show result sol.ap # Loads nEfficients nVariables nInputs nOutputs Inputs Outputs # 4 0.6666667 2 4 2 2 Employees, Depreciation CarsSold, WorkOrders # 3 0.9575672 2 3 1 2 Depreciation CarsSold, WorkOrders # 2 1.0000000 1 2 1 1 Depreciation CarsSold # Summary the model with 3 variables summary(sol.ap$models[[3]]) # Model name # Orientation input # Load orientation inoutput # Model load 0.957567163474156 # Input load.Depreciation 1 # Output load.CarsSold 1.04243283652584 # Output load.WorkOrders 0.957567163474156 # Inputs Depreciation # Outputs CarsSold WorkOrders # nInputs 1 # nOutputs 2 # nVariables 3 # nEfficients 2 # Eff. Mean 0.90022318389575 # Eff. sd 0.135194867030839 # Eff. Min. 0.651504424778761 # Eff. 1st Qu. 0.872252747252747 # Eff. Median 0.942225031605563 # Eff. 3rd Qu. 0.997898230088496 # Eff. Max. 1 # Get efficiencies for the model with 3 variables sol.ap$models[[3]]$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044
Stepwise procedure for variable selection in DEA models.
adea_stepwise( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), load.critical = 0.5, max.steps = ncol(input) + ncol(output) - 2, solver = "auto", verbose = 0 )adea_stepwise( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", direction = c("backward", "backward/input", "backward/output"), load.critical = 0.5, max.steps = ncol(input) + ncol(output) - 2, solver = "auto", verbose = 0 )
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. |
direction |
The direction in which the variables enter or exit the model. Currently, only the "backward" option is implemented. |
load.critical |
Minimum values for loads to consider that a variable should be considered in the model. It can be also a vector with two values, the first value input loads and the second for output loads. |
max.steps |
The maximum number of steps allowed. |
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 |
verbose |
Use 0 for minimal output, displaying only the final model. Use 1 or higher values to get detailed information for each step. The default is 0. This option affects only the printed output and not the result. |
This function serves as a backend utility for variable selection in DEA models and is not intended for end-user use. It is used as part of the adea_hierarchical and adea_parametric functions.
This function performs a stepwise procedure for variable selection within DEA models.
The function returns a DEA model with optimised set of variables.
This function calculates an efficiency score for each DMU and computes a load for each variable within the current model. However, it's essential to note that the loads or contributions of input or output variables are subject to constraints within specified values. As a result, the efficiencies of DMUs may deviate from those obtained in regular DEA or ADEA models.
cadea( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", load.min, load.max, solver = "lpsolve" )cadea( input, output, orientation = c("input", "output"), load.orientation = c("inoutput", "input", "output"), name = "", load.min, load.max, solver = "lpsolve" )
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. |
load.min |
A numeric value or vector giving minimum values for loads.
Values for |
load.max |
A numeric value or vector giving maximum values for loads.
Values for |
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 |
A variable load is a numerical value between 0 and 1, with 0 signifying that the variable's contribution to the efficiency calculations is negligible. In an ideal scenario, each input or output variable would have a load of 1. This model enforces input and output weights in a manner that ensures the final variable loads fall within specified values.
In a raw variable selection procedure, it's possible to inadvertently remove a variable from a DEA model, leading to a non-natural model. In other cases, there may be political or tactical reasons for certain variables to be considered. In a standard DEA model, the weights associated with these variables might be reduced to very small values, effectively rendering their contributions nearly negligible.
The constraints for variable loads in these models prevent such scenarios by ensuring that the contributions of variables reach the desired levels. This maintains the integrity and significance of variables in the DEA model.
For more information about loads or ADEA model see adea
The function returns a cadea object with the follosing 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
load.min: Miniminum allowed value for variable loads when load.orientation is ioutput, for input variable loads when load.orientation is input, and for output variable loads when load.orientation is output.
load.max: Mamixum allowed value for all, input or output variable loads as for load.min.
ux: A set of weights for inputs
vy: A set of weights for output
iterations: Number of iterations to reach the stop rule
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
efficiency scores, one set of weights for inputs and other for outputs, number of efficient units, variable loads and model load.
solver: The solver used for the resolution of the optimization problem
If the given limits are too narrow, then the model is infeasible, which will result in an error.
data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute adea model model <- adea(input, output) 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 input variable loads model$loads$input # Employees Depreciation # 0.6666667 1.3333333 # Get output variable loads model$loads$output # CarsSold WorkOrders # 1.2663476 0.7336524 # Compute a constrained adea model to force load between .8 and 1.5 cmodel <- cadea(input, output, load.min = .8, load.max = 1.5) cmodel # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.5920826 # Get loads cmodel$loads # $load # [1] 0.8 # $input # Employees Depreciation # 0.8 1.2 # $iinput # Employees # 1 # $output # CarsSold WorkOrders # 1.2 0.8 # $ioutput # WorkOrders # 2 # $load.min # [1] 0.8 0.8 0.8 0.8 # $load.max # [1] 1.5 1.5 1.5 1.5 # See differences of efficiencies in both models model$eff - cmodel$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # -2.220446e-16 -1.332268e-15 -1.110223e-16 2.220446e-16 -1.110223e-16 5.942183e-02data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute adea model model <- adea(input, output) model # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Get input variable loads model$loads$input # Employees Depreciation # 0.6666667 1.3333333 # Get output variable loads model$loads$output # CarsSold WorkOrders # 1.2663476 0.7336524 # Compute a constrained adea model to force load between .8 and 1.5 cmodel <- cadea(input, output, load.min = .8, load.max = 1.5) cmodel # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.5920826 # Get loads cmodel$loads # $load # [1] 0.8 # $input # Employees Depreciation # 0.8 1.2 # $iinput # Employees # 1 # $output # CarsSold WorkOrders # 1.2 0.8 # $ioutput # WorkOrders # 2 # $load.min # [1] 0.8 0.8 0.8 0.8 # $load.max # [1] 1.5 1.5 1.5 1.5 # See differences of efficiencies in both models model$eff - cmodel$eff # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # -2.220446e-16 -1.332268e-15 -1.110223e-16 2.220446e-16 -1.110223e-16 5.942183e-02
An example dataset with six car dealers data to be use in DEA (Data Envelopment Analysis).
Employees: The number of employees in the car dealer to be considered as input variable in DEA.
Sold: The sold amount by the car dealer to be considered as output variable in DEA.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis). DEA rate each unit, in this case car dealers, in terms of efficiency. Less input and more output lead to higher efficiency scores.
data('cardealers1')
Vicente Coll Serrano y Olga M. Blasco Blasco (2006) Evaluacion de la eficiencia mediante el analisis envolvente de datos. Electronic edition. https://www.eumed.net/libros-gratis/2006c/197/
See also adea-package.
An example dataset with six car dealers data to be use in DEA (Data Envelopment Analysis).
Employess: The number of employees in the car dealer to be considered as input variable in DEA.
CarsSold: The number of car sold by the car dealer to be considered as output variable in DEA.
WorkOrders: The number of works orders for the mechanical garage to be considered as output variable in DEA.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis). DEA rate each unit, in this case car dealers, in terms of efficiency. Less input and more output lead to higher efficiency scores.
data('cardealers2')
Vicente Coll Serrano y Olga M. Blasco Blasco (2006) Evaluacion de la eficiencia mediante el analisis envolvente de datos. Electronic edition. https://www.eumed.net/libros-gratis/2006c/197/
See also adea-package.
An example dataset with six car dealers data to be use in DEA (Data Envelopment Analysis).
Employess: The number of employees in the car dealer to be considered as input variable in DEA.
Amortization: As an indirect measure of the capital invested to be considered as input variable in DEA.
NetSales: Net amount of sales to be considered as output variable in DEA.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis). DEA rate each unit, in this case car dealers, in terms of efficiency. Less input and more output lead to higher efficiency scores.
data('cardealers3')
Vicente Coll Serrano y Olga M. Blasco Blasco (2006) Evaluacion de la eficiencia mediante el analisis envolvente de datos. Electronic edition. https://www.eumed.net/libros-gratis/2006c/197/
See also adea-package.
An example dataset with six car dealers to be use in DEA (Data envelopment analysis).
Employees: Number of employees to be considered as input variable in DEA.
Depreciation: Depreciation of stored to be considered as input variable in DEA.
Sold: Number of cars sold as output variable in DEA.
Orders: Number of work orders in garage as output variable in DEA.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis). DEA rate each unit, in this case car dealers, in terms of efficiency. Less input and more output lead to higher efficiency scores.
data('cardealers4')
Vicente Coll Serrano y Olga M. Blasco Blasco (2006) Evaluacion de la eficiencia mediante el analisis envolvente de datos. Electronic edition. https://www.eumed.net/libros-gratis/2006c/197/
See also adea-package.
Data Envelopment Analysis, DEA, computes, for a set of Decision Making Units, DMU, a relative efficiency score, comparing one unit with the others.
dea( input, output, orientation = c("input", "output"), name = "", solver = "auto" )dea( input, output, orientation = c("input", "output"), name = "", solver = "auto" )
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". |
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 |
Each DMU transforms inputs into outputs. The set of inputs and outputs is the same for all the DMUs, but not their quantities.
This function computes a relative efficiency score and weights for each input and output variable in the model. All these for each DMU.
This function return a dea class object with the following named members:
name: A label of the model
orientation: DEA model orientation 'input' or 'output'
inputnames: Variable input names
outputnames: Variable output names
eff: is a vector with DMU's scores
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
# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute dea model model <- dea(input, output, name = 'DEA for cardealers4 dataset') # Print DMU efficiencies 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 # Summarize the model and print aditional information summary(model) # Model name DEA for cardealers4 dataset # Orientation input # 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. 0.997898230088496 # Eff. Max. 1# Load data data('cardealers4') # Define input and output input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute dea model model <- dea(input, output, name = 'DEA for cardealers4 dataset') # Print DMU efficiencies 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 # Summarize the model and print aditional information summary(model) # Model name DEA for cardealers4 dataset # Orientation input # 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. 0.997898230088496 # Eff. Max. 1
Data Envelopment Analysis (DEA) calculates a relative efficiency score for a set of Decision Making Units (DMUs) by comparing one unit with others.
fsdea( input, output, orientation = c("input", "output"), name = "", ninputs = ncol(input), noutputs = ncol(output), nvariables = ncol(input) + ncol(output), solver = "auto" )fsdea( input, output, orientation = c("input", "output"), name = "", ninputs = ncol(input), noutputs = ncol(output), nvariables = ncol(input) + ncol(output), solver = "auto" )
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". |
name |
An optional descriptive name for the model. The default is an empty string. This name will be displayed in printed and summarized results. |
ninputs |
Number of input features (variables) to be selected. Default is the number of input variables. |
noutputs |
Number of output features (variables) to be selected. Default is the number of output variables. |
nvariables |
Number of total features (variables) to be selected, only applicable when both ninputs and noutputs are omitted. Default is the number of input plus output variables. |
solver |
The solver to be used by ROI to solve the DEA optimization problem. The solver must be installed and capable of solving mixed integer linear programming problems. Default is "auto." Use 'ROI_installed_solvers()' to list available solvers. |
Each DMU transforms inputs into outputs. The set of inputs and outputs is the same for all the DMUs, but not their quantities.
One of the fundamental steps in the application of data envelopment analysis is the choice of variables to include in the model. One of the methods proposed for this is what is known as the feature selection method. This method constructs a linear programming problem to maximize some objective function related to the dmu efficiencies. This function implements the feature selection method in the article [Benitez-Pena, S., Bogetoft, P. and Romero Morales, D. *Feature Selection in Data Envelopment Analysis: A Mathematical Optimization approach* Omega, Elsevier BV, **2020**, Vol. 96, pp. 102068](http://www.sciencedirect.com/science/article/pii/S0305048318312131)
This function, in the case of input orientation, maximize the sum of all efficiencies, while in the output orientation case, the goal is to minimize this sum. Once the relevant variables are selected, the function calculates the relative efficiency scores for each Decision Making Unit (DMU) and determines the weights for all input and output variables within the model.
This function return a fsdea class object with the following named members:
orientation: DEA model orientation.
name: A label of the model.
ninputs: Number of inputs to be selected.
noutputs: Number of outputs to be selected.
nvariables: Number of total variables to be selected.
inputnames: Names of input variables.
outputnames: Names of output variables.
eff: A vector with DMU scores.
ux: A set of weights for input variables.
vy: A set of weights for output variables.
obj: Optimal value of the objective function in the optimization problem.
iselected: A vector of zeros and ones indicating the selected input variables.
oselected: A vector of zeros and ones indicating the selected output variables.
niselected: Number of input selected variables.
noselected: Number of output selected variables.
nvselected: Number of selected variables.
vinput: Standardized virtual input divided by the sum of the weights, see [Costa2006] in adea-package.
voutput: Standardized virtual output divided by the sum of the weights, see [Costa2006] in adea-package.
solver: The solver used for the resolution of the optimization problem.
data('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute DEA model selecting at most 1 output model1o <- fsdea(input, output, noutputs = 1) model1o # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.7875000 0.7500000 0.3000000 0.8653846 1.0000000 0.5400000 # Selected inputs : Depreciation # Selected outputs: CarsSold # Compute DEA model selecting at most 1 input model1i <- fsdea(input, output, ninputs = 1) model1i # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Selected inputs : Depreciation # Selected outputs: CarsSold, WorkOrders # Compute DEA model selecting at most 3 variables model3v <- fsdea(input, output, nvariables = 3) model3v # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Selected inputs : Depreciation # Selected outputs: CarsSold, WorkOrdersdata('cardealers4') input <- cardealers4[, c('Employees', 'Depreciation')] output <- cardealers4[, c('CarsSold', 'WorkOrders')] # Compute DEA model selecting at most 1 output model1o <- fsdea(input, output, noutputs = 1) model1o # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.7875000 0.7500000 0.3000000 0.8653846 1.0000000 0.5400000 # Selected inputs : Depreciation # Selected outputs: CarsSold # Compute DEA model selecting at most 1 input model1i <- fsdea(input, output, ninputs = 1) model1i # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Selected inputs : Depreciation # Selected outputs: CarsSold, WorkOrders # Compute DEA model selecting at most 3 variables model3v <- fsdea(input, output, nvariables = 3) model3v # Dealer A Dealer B Dealer C Dealer D Dealer E Dealer F # 0.9915929 1.0000000 0.8928571 0.8653846 1.0000000 0.6515044 # Selected inputs : Depreciation # Selected outputs: CarsSold, WorkOrders
ADEA plot of standarized virtual input and virtual output
## S3 method for class 'adea' plot( x, main = NULL, xlab = NULL, ylab = NULL, labels = NULL, labels.pos = 4, lcol = "black", ... )## S3 method for class 'adea' plot( x, main = NULL, xlab = NULL, ylab = NULL, labels = NULL, labels.pos = 4, lcol = "black", ... )
x |
ADEA object to be plotted |
main |
if not null then it is used as main in plot. Its default value is the translation of "ADEA efficient frontier". If the adea x has name it is added to the previous value. |
xlab |
if not null then it is used as xlab in plot. Its default value is the translation of "Virtual input". |
ylab |
if not null then it is used as ylab in plot. Its default value is the translation of "Virtual output". |
labels |
if not null then a vector of labels for the DMUs points |
labels.pos |
position for the labels in the plot. Its default value is 4. |
lcol |
the color to use to draw the line. Its default value is black. |
... |
Adittional parameters to plot |
This function plots virtual input and virtual outpus in an ADEA model. The virtual input and output vectors are computed as a weighted sum of the inputs and outputs. In addition, it is imposed that the sum of the weights be the unit.
For more information on this calculation process see the references in adea-package.
For the calculations of virtual input and virtual output, the weights generated by ADEA have been used, but they are the same as those that would be obtained using standard DEA.
A list with vinput and voutput values. These values are provided mainly for use with the function identify.
data("cardealers4") input = cardealers4[, c('Employees', 'Depreciation')] output = cardealers4[, c('CarsSold', 'WorkOrders')] adea <- adea(input = input, output = output) plot(adea)data("cardealers4") input = cardealers4[, c('Employees', 'Depreciation')] output = cardealers4[, c('CarsSold', 'WorkOrders')] adea <- adea(input = input, output = output) plot(adea)
Print method for adea class
## S3 method for class 'adea' print(x, ...)## S3 method for class 'adea' print(x, ...)
x |
Object of class adea to print. |
... |
Optional arguments to "print". |
For the final model of adea_hierarchical function prints a summary, the input variables, and outputs variables.
## S3 method for class 'adeahierarchical' print(x, ...)## S3 method for class 'adeahierarchical' print(x, ...)
x |
Object of class adeahierarchical to print. |
... |
Optional arguments to "print". |
Print adealoadleverage results in human readable way
## S3 method for class 'adealoadleverage' print(x, ...)## S3 method for class 'adealoadleverage' print(x, ...)
x |
Object of class adealoadleverage to print. |
... |
Optional arguments to "print". |
For the final model of adea_parametric function prints a summary, the input variables, and outputs variables.
## S3 method for class 'adeaparametric' print(x, ...)## S3 method for class 'adeaparametric' print(x, ...)
x |
Object of class adeaparametric to print. |
... |
Optional arguments to "print". |
For the final model of adeastepwise function prints a summary, the input variables, and outputs variables.
## S3 method for class 'adeastepwise' print(x, ...)## S3 method for class 'adeastepwise' print(x, ...)
x |
Object of class stepwise to print. |
... |
Optional arguments to "print". |
Print method for cadea class
## S3 method for class 'cadea' print(x, ...)## S3 method for class 'cadea' print(x, ...)
x |
Object of class cadea to print. |
... |
Optional arguments to "print". |
Print method for dea class
## S3 method for class 'dea' print(x, ...)## S3 method for class 'dea' print(x, ...)
x |
Object of class dea to print. |
... |
Optional arguments to "print". |
Print method for fsdea class
## S3 method for class 'fsdea' print(x, ...)## S3 method for class 'fsdea' print(x, ...)
x |
Object of class fsdea to print. |
... |
Optional arguments to "print". |
Data set spanishuniversities2018 belongs to 47 public Spanish universities, all but Pais Vasco because its staff data is missing.
TeachingStaff: number of people teaching and researching with a doctor degree.
FPU2018: number of predoctoral contracts with state funds done in 2018.
FPI2018: number of postdoctoral contracts with state funds done in 2018.
Patents: number of patents registered from 2013 and 2017.
PhDThesis: number of PhD Thesis in 2017/2018 academic year.
JCR: number of papers published in journals included in JCR index
Six: number of positive reports obtained in the state research evaluation program. All permanent teaching staff from Spanish universities can apply every six year for a program to get a positive evaluation of their research activities. Positive evaluations are considered merits for promotion and represent an increase in salary.
Projects: number of research projects financed with state funds obtained in competitive calls.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis).
The only one input variable is TeachingStaff.
The output variables are: TeachingStaff, FPU2018, FPI2018, Patens, PhDThesis, JCR, Six and Projects.
data('spanishuniversities2018')
Data are taken from public available information systems.
See also adea-package.
Extract information from a fsdea class object and compute some more. The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
## S3 method for class 'adea' summary(object, ...)## S3 method for class 'adea' summary(object, ...)
object |
is the object of class adea to summarise |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
For the final model of adea_hierarchical function print the model name, orientation, load orientation, a summary, the input variables, and outputs variables.
## S3 method for class 'adeahierarchical' summary(object, ...)## S3 method for class 'adeahierarchical' summary(object, ...)
object |
Is the object of class adeahierarchical to summarise. |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
For the final model of adea_parametric function print the model name, orientation, load orientation, a summary, the input variables, and outputs variables.
## S3 method for class 'adeaparametric' summary(object, ...)## S3 method for class 'adeaparametric' summary(object, ...)
object |
is the object of class adeaparametric to summarise |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
For the final model of adea_stepwise function print the model name, orientation, load orientation, a summary, the input variables, and outputs variables.
## S3 method for class 'adeastepwise' summary(object, ...)## S3 method for class 'adeastepwise' summary(object, ...)
object |
Is the object of class adeastepwise to summarise. |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
Extract information from a fsdea class object and compute some more. The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
## S3 method for class 'cadea' summary(object, ...)## S3 method for class 'cadea' summary(object, ...)
object |
is the object of class cadea to summarise |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
Extract information from a dea class object and compute some more.
## S3 method for class 'dea' summary(object, ...)## S3 method for class 'dea' summary(object, ...)
object |
is the object of class dea to summarise |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
This function returns the following information, as a named list:
Model name: if it is previously set
Orientation: Model orientation
Inputs: Names of the input variables in the model
Outputs: Names of the output variables in the model
nInputs: Number of the input variables in the model
nOutputs: Number of the output variables in the model
nVariables: Total number of input and output variables in the model
n: Number of DMUs
nEfficients: Number of efficient DMUs taking into account whithin eff.tolerance tolerance.
Mean: Mean of efficiency scores.
sd: Standard deviation of efficiency scores.
Min.: Minimun value of efficiency scores.
1st Qu.: First quater of efficiency scores.
Median: Median of efficiency scores.
3rd Qu.: Third quater of efficiency scores.
Max.: Maximum value of efficiency scores.
Extract information from a fsdea class object and compute some more. The default tolerance to consider a DMU as efficient one is .001 in reports. Use 'eff.tolerance' parameter to consider another tolerance between 0 and 1.
## S3 method for class 'fsdea' summary(object, ...)## S3 method for class 'fsdea' summary(object, ...)
object |
is the object of class dea to summarise |
... |
For compatibility reason, see note about 'eff.tolerance' parameter. |
This function returns the following information, as a named vector:
Model name: if it is previously set
Orientation: Model orientation
Inputs: Names of the input variables in the model
Outputs: Names of the output variables in the model
n: Number of DMUs
nEfficients: Number of efficient DMUs taking into account whithin eff.tolerance tolerance.
Mean: This and following statistical measure of the efficiency scores. Its mean.
sd: Its standard deviation.
Min.: Its minimun value.
1st Qu.: Its first quater.
Median: Its median.
3rd Qu.: Its third quater.
Max.: Its maximum value.
nInputs: Number of input variables to select
nOutputs: Number of output variables to select
nTotal: Total number of variables to select
iSelected: Names of the selected input variables
oSelected: Names of the selected output variables
tokyo_libraries involves a set of 23 libraries in Tokyo and it has been used frequently in DEA literature.
Area.I1: Area of library.
Books.I2: Number of books.
Staff.I3: Staff members.
Populations.I4: Population of influence area.
Regist.O1: Registered people.
Borrow.O2: Borrowed books.
The purpose of this dataframe is to be used in DEA (Data Envelopment Analysis).
The input variables are Area.I1, Books.I2, Staff.I3 and Populations.I4.
The output variables are Regist.O1 and Borrow.O2.
data('tokyo_libraries')
See also adea-package.