TY - JOUR

T1 - LASSO+DEA for small and big wide data

AU - Chen, Ya

AU - Tsionas, Mike G.

AU - Zelenyuk, Valentin

N1 - This is the author’s version of a work that was accepted for publication in Omega. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Omega, 102, 2021 DOI: 10.1016/j.omega.2021.102419

PY - 2021/7/31

Y1 - 2021/7/31

N2 - In data envelopment analysis (DEA), the curse of dimensionality problem may jeopardize the accuracy or even the relevance of results when there is a relatively large dimension of inputs and outputs, even for relatively large samples. Recently, a machine learning approach based on the least absolute shrinkage and selection operator (LASSO) for variable selection was combined with sign-constrained convex nonparametric least squares (SCNLS, a special case of DEA), and dubbed as LASSO-SCNLS, as a way to circumvent the curse of dimensionality problem. In this paper, we revisit this interesting approach, by considering various data generating processes. We also explore a more advanced version of LASSO, the so-called elastic net (EN) approach, adapt it to DEA and propose the EN-DEA. Our Monte Carlo simulations provide additional and to some extent, new evidence and conclusions. In particular, we find that none of the considered approaches clearly dominate the others. To circumvent the curse of dimensionality of DEA in the context of big wide data, we also propose a simplified two-step approach which we call LASSO+DEA. We find that the proposed simplified approach could be more useful than the existing more sophisticated approaches for reducing very large dimensions into sparser, more parsimonious DEA models that attain greater discriminatory power and suffer less from the curse of dimensionality.

AB - In data envelopment analysis (DEA), the curse of dimensionality problem may jeopardize the accuracy or even the relevance of results when there is a relatively large dimension of inputs and outputs, even for relatively large samples. Recently, a machine learning approach based on the least absolute shrinkage and selection operator (LASSO) for variable selection was combined with sign-constrained convex nonparametric least squares (SCNLS, a special case of DEA), and dubbed as LASSO-SCNLS, as a way to circumvent the curse of dimensionality problem. In this paper, we revisit this interesting approach, by considering various data generating processes. We also explore a more advanced version of LASSO, the so-called elastic net (EN) approach, adapt it to DEA and propose the EN-DEA. Our Monte Carlo simulations provide additional and to some extent, new evidence and conclusions. In particular, we find that none of the considered approaches clearly dominate the others. To circumvent the curse of dimensionality of DEA in the context of big wide data, we also propose a simplified two-step approach which we call LASSO+DEA. We find that the proposed simplified approach could be more useful than the existing more sophisticated approaches for reducing very large dimensions into sparser, more parsimonious DEA models that attain greater discriminatory power and suffer less from the curse of dimensionality.

U2 - 10.1016/j.omega.2021.102419

DO - 10.1016/j.omega.2021.102419

M3 - Journal article

VL - 102

JO - Omega

JF - Omega

SN - 0305-0483

M1 - 102419

ER -