An alternative approach to handle high dimensionality in DEA: Consumption efficiency analysis in Malaysia car market

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.