Quantile Data Envelopment Analysis.

qDEA: Quantile Data Envelopment Analysis

Overview

The qDEA package provides functions for quantile Data Envelopment Analysis (qDEA), extending traditional DEA methods to allow for a specified proportion of observations to lie outside the production frontier. This approach is particularly useful for robust efficiency analysis in the presence of outliers or noise.

Installation

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

install.packages("qDEA")

Key Features

• Standard DEA and qDEA estimation: Compute efficiency scores using various DEA models
• Multiple orientations: Input-oriented, output-oriented, graph (input-output), hyperbolic, and directional distance function models
• Returns to scale: Support for CRS, VRS, DRS, and IRS specifications
• Bias correction: Bootstrap-based bias correction procedures
• Iterative qDEA: Automatic convergence testing for qDEA solutions
• Peer identification: Identify efficient peers and compute projection values
• LP solvers: Integration with the highs solver

Basic Usage

library(qDEA)

# Load example data
data(CST11)

# Prepare input and output matrices
X <- as.matrix(CST11$EMPLOYEES)
Y <- as.matrix(CST11$SALES)

# Run basic DEA (output-oriented, CRS)
result <- qDEA(X = X, Y = Y, orient = "out", RTS = "CRS")

# View efficiency scores
result$effvals

# Run qDEA with 10% outliers allowed
result_q <- qDEA(X = X, Y = Y, qout = 0.10, orient = "out", RTS = "CRS")

# View qDEA efficiency scores
result_q$effvalsq

Advanced Features

Bootstrap Bias Correction

# Run qDEA with bootstrap bias correction
result_boot <- qDEA(X = X, Y = Y, 
                    qout = 0.10, 
                    nboot = 100,
                    orient = "out", 
                    RTS = "VRS")

# Access bias-corrected estimates
result_boot$BOOT_DATA$effvalsq.bc

Multiple Inputs and Outputs

# Load two-input, two-output example
data(CST22)

X <- as.matrix(CST22[, c("DOCTORS", "NURSES")])
Y <- as.matrix(CST22[, c("OUT_PATIENTS", "IN_PATIENTS")])

# Run qDEA
result <- qDEA(X = X, Y = Y, qout = 0.05, orient = "in", RTS = "VRS")

Methodology

The qDEA method extends traditional DEA by allowing a pre-specified proportion (α) of observations to lie outside the estimated production frontier. This makes the method more robust to outliers and measurement error while maintaining computational efficiency through linear programming.

Key References

• Atwood, J., and S. Shaik. (2020). "Theory and Statistical Properties of Quantile Data Envelopment Analysis." European Journal of Operational Research, 286:649-661. DOI: 10.1016/j.ejor.2020.03.054

• Atwood, J., and S. Shaik. (2018). "Quantile DEA: Estimating qDEA-alpha Efficiency Estimates with Conventional Linear Programming." In Productivity and Inequality. Springer Press. DOI: 10.1007/978-3-319-68678-3_4

Getting Help

For questions and issues, please contact the package maintainer at [email protected].

License

GPL-2 | GPL-3