A non-parametric and multidirectional model in quantitative research

Authors

  • Kelly Murillo Centro de Investigacao e Desenvolvimento em Matemática e Aplicacoes (CIDMA), Departamento de Matemática, Universidade de Aveiro, Portugal.
  • Eugénio Alexander Miguel Rocha Centro de Investigacao e Desenvolvimento em Matemática e Aplicacoes (CIDMA), Departamento de Matemática, Universidade de Aveiro, Portugal.

DOI:

https://doi.org/10.17268/sel.mat.2021.02.03

Keywords:

Multidirectional efficiency analysis, NC value, dimensionality test, cluster analysis, fit model, manufacturing sector.

Abstract

In this work, a non-parametric and deterministic approach based on multidirectional efficiency analysis

(MEA) is presented. The proposed model involves MEA with other important mathematical techniques in data analysis, such as the calculation of the NC value for the analysis of groups with different levels of

efficiency. This model allows us to examine the factors that influence the behavior of decision-making units in different contexts such as business efficiency, educational quality, energy efficiency, circular economy, among others. Particularly in this work, we show the results obtained in 1787 Portuguese companies in the materials manufacturing sector (manufacture of wood and paper; manufacture of rubber products, plastics and other non-metallic mineral products; manufacture of common metals and metallic products, except machinery and equipment) in an eight-year period (2006-2013) of study. The results allow, not only a characterization of the financial structure of the sector and a diagnosis through indices that identify the strategic positioning of companies in terms of efficiency scores; but also a characterization of the most efficient units and an analysis of the variables that must be addressed differently, to obtain better results, in terms of economic performance.

References

Abdi H, Williams LJ. Principal Component Analysis. Wiley Interdisciplinary Reviews: Computational Statistics; 2010; 2(4):433–59. doi:10.1002/wics.101.

Abood S. Quality of imrovement initiative in nursing homes. Am J Nurs [Internet]. [Consultado 22 Nov 2012]; 2002; 102(6). Disponible en: http://www.nursingworld.org.

Asmild M, Baleˇzentis T, Hougaard JL. Multi-directional Productivity Change: MEA Malmquist, Journal of Productivity Analysis, 2016; 46: 109–119.

Asmild M, Holvad T, Hougaard J, Kronborg D. Railway reforms: do they influence operating efficiency? Transportation, 2009; 36(5): 617-638.

Banker RD, Charnes A, Cooper W. Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science, 2009; 30(9), 1078–92. doi:10.1287/mnsc.30.9.1078.

Bogetoft P, Hougaard JL. Efficiency Evaluations Based on Potential (Non-proportional) Improvements. Journal of Productivity Analysis, 1999; 12(3):233–47. doi:10.1023/A:1007848222681.

Dawes J, González-Parra G, Rowley J. Enhancing the customer experience: contributions from information technology, J Business Res. 2005; 36(5):350-7.

Dray S. On the Number of Principal Components: A Test of Dimensionality Based on Measurements of Similarity Between Matrices. Computational Statistics and DataAnalysis, 2008; 52(4): 2228–37. doi:10.1016/j.csda.2007.07.015

Evangelista A, Ortiz A, Ríos-Soto K, Urdapilleta A. USA the fast food nation: Obesity as an epidemic. Los Alamos National Laboratory; 2004.

Gongbing B, Pingchun W, Feng Y, Liang L, Energy and Environmental Efficiency of China’s Transportation Sector: A Multidirectional Analysis Approach. Mathematical Problems in Engineering, 2014; 1-12. Article ID 539596. doi:10.1155/2014/539596

Hirschberg JG, Lye JN. Conglomeradoing in a Data Envelopment Analysis Us-ing Bootstrapped Efficiency Scores (Department of Economics - Working Papers Series No. 800). The University of Melbourne. 2001.

Hougaard JL, Kronborg D, Overgard, C. Improvement Potential in Danish Elderly Care. Health Care Management Science, 2004; 7(3): 225–235.

Inman HF, Bradley Jr EL. The over- lapping coefficient as a measure de agreement between probability distributions and point estimation de the overlap of two normal densities, Communications in Statistics, Theory and Methods, 1989; 18(10): 3851-3874.

Karun K, Isaac E. Cogitative Analysis on k-means Conglomeradoing Algorithm and its Variants. International Journal of Advanced Research in Computer and Communication Engineering, 2013; 2(4):1875–80.

Pearson K. On Lines and Planes of Closest Fit to Systems of Points in Space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1901; 2(11): 559–72. doi:10.1080/14786440109462720.

Wang K, Yu S, Li MJ, Wei Y. Multi-directional efficiency analysis-based regional industrial environmental performance evaluation of China. Natural Hazards. 2015.

Walesiak M. Multivariate Statistical Analysis in Marketing Research (Research Papers No. 654). Wroclaw University of Economics Supplement, 1993; 75(2): 273-299. http://dx.doi.org/10.1007/s11069-014-1097-4

Romero S, Moreno FJ, Rodriguez IM. Linear Partial Differential Equations for Engineers and Scientists. 2th. ed. Boca Raton: Chapman & Hall/CRC; 2002.

Thomas D, Weedermann M, Fuemmeler B, Martin C, Dhurandhar N, Bredlau C, Bouchard C. Dynamic model predicting overweight, obesity, and extreme obesity prevalence trends. Obesity. 2014; 22(2):590-597.

Published

2021-12-27

How to Cite

Murillo, K. ., & Miguel Rocha, E. A. (2021). A non-parametric and multidirectional model in quantitative research. Selecciones Matemáticas, 8(02), 235-247. https://doi.org/10.17268/sel.mat.2021.02.03