### Abstract

Being non-parametric, data envelopment analysis (DEA) suffers from the curse of dimensionality, especially when large sample size is not attainable. This entails indiscriminate efficiency estimates, thus complicates the benchmarking process. Principal component analysis (PCA) is a well-known remedy for dimension reduction. However, as principal components are uncorrelated, the eigenvectors are orthogonal. This implies the existence of positive and negative weights of the principal components, and subsequently, it violates the disposability assumption in DEA. To overcome this problem, modifications to the principal components are suggested. With a varimax rotation, a simple structure is sought so that the variables can be segregated into two groups, one exhibits positive correlation and the other negative correlation with a principal component. To avoid contrast variables in a component with minimal loss of information, the group that has a smaller amount of explained variation will be discarded. By taking the normalized absolute value of these modified vectors, components can be constructed as weighted averages of the original variables. It is illustrated that the proposed modifications work well in the consumption efficiency analysis of Malaysia car market. Redundancy analysis shows that the modified components preserve the same amount (> 90%) of explained variance extracted by a PCA procedure, thus justifies the use of the modified components to replace the original variables. As this involves a smaller dimension of components without contrast variables, it is shown that the proposed modification is more discriminating than that of the standard DEA.

Original language | English |
---|---|

Pages (from-to) | 52-65 |

Number of pages | 14 |

Journal | International Journal of Applied Mathematics and Statistics |

Volume | 25 |

Issue number | 1 |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- Data envelopment analysis
- Efficiency
- Principal component analysis
- Redundancy
- Varimax rotation

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**An alternative approach to handle high dimensionality in DEA : Consumption efficiency analysis in Malaysia carmarket.** / Yap, G. L C; Ismail, Wan Rosmanira; Isa, Zaidi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An alternative approach to handle high dimensionality in DEA

T2 - Consumption efficiency analysis in Malaysia carmarket

AU - Yap, G. L C

AU - Ismail, Wan Rosmanira

AU - Isa, Zaidi

PY - 2012

Y1 - 2012

N2 - Being non-parametric, data envelopment analysis (DEA) suffers from the curse of dimensionality, especially when large sample size is not attainable. This entails indiscriminate efficiency estimates, thus complicates the benchmarking process. Principal component analysis (PCA) is a well-known remedy for dimension reduction. However, as principal components are uncorrelated, the eigenvectors are orthogonal. This implies the existence of positive and negative weights of the principal components, and subsequently, it violates the disposability assumption in DEA. To overcome this problem, modifications to the principal components are suggested. With a varimax rotation, a simple structure is sought so that the variables can be segregated into two groups, one exhibits positive correlation and the other negative correlation with a principal component. To avoid contrast variables in a component with minimal loss of information, the group that has a smaller amount of explained variation will be discarded. By taking the normalized absolute value of these modified vectors, components can be constructed as weighted averages of the original variables. It is illustrated that the proposed modifications work well in the consumption efficiency analysis of Malaysia car market. Redundancy analysis shows that the modified components preserve the same amount (> 90%) of explained variance extracted by a PCA procedure, thus justifies the use of the modified components to replace the original variables. As this involves a smaller dimension of components without contrast variables, it is shown that the proposed modification is more discriminating than that of the standard DEA.

AB - Being non-parametric, data envelopment analysis (DEA) suffers from the curse of dimensionality, especially when large sample size is not attainable. This entails indiscriminate efficiency estimates, thus complicates the benchmarking process. Principal component analysis (PCA) is a well-known remedy for dimension reduction. However, as principal components are uncorrelated, the eigenvectors are orthogonal. This implies the existence of positive and negative weights of the principal components, and subsequently, it violates the disposability assumption in DEA. To overcome this problem, modifications to the principal components are suggested. With a varimax rotation, a simple structure is sought so that the variables can be segregated into two groups, one exhibits positive correlation and the other negative correlation with a principal component. To avoid contrast variables in a component with minimal loss of information, the group that has a smaller amount of explained variation will be discarded. By taking the normalized absolute value of these modified vectors, components can be constructed as weighted averages of the original variables. It is illustrated that the proposed modifications work well in the consumption efficiency analysis of Malaysia car market. Redundancy analysis shows that the modified components preserve the same amount (> 90%) of explained variance extracted by a PCA procedure, thus justifies the use of the modified components to replace the original variables. As this involves a smaller dimension of components without contrast variables, it is shown that the proposed modification is more discriminating than that of the standard DEA.

KW - Data envelopment analysis

KW - Efficiency

KW - Principal component analysis

KW - Redundancy

KW - Varimax rotation

UR - http://www.scopus.com/inward/record.url?scp=84855752168&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855752168&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 52

EP - 65

JO - International Journal of Applied Mathematics and Statistics

JF - International Journal of Applied Mathematics and Statistics

SN - 0973-1377

IS - 1

ER -