A slacks-based measure of super-efficiency in data envelopment analysis

In most models of Data Envelopment Analysis (DEA), the best performers have the full efficient status denoted by unity (or 100%), and, from experience, we know that usually plural Decision Making Units (DMUs) have this “efficient status”. To discriminate between these efficient DMUs is an interesting subject. This paper addresses this “super-efficiency” issue by using the slacks-based measure (SBM) of efficiency, which the author proposed in his previous paper [European Journal of Operational Research 130 (2001) 498]. The method differs from the traditional one based on the radial measure, e.g. Andersen and Petersen model, in that the former deals directly with slacks in inputs/outputs, while the latter does not take account of the existence of slacks. We will demonstrate the rationality of our approach by comparing it with the radial measure of super-efficiency. The proposed method will be particularly useful when the number of DMUs are small compared with the number of criteria employed for evaluation.

A Slacks-based Measure of Super-Efficiency in Data Envelopment Analysis

Advanced Statistical Methods in Biometric Research.

In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

Partial least squares (PLS) has been introduced as a “causal-predictive” approach to structural equation modeling (SEM), designed to overcome the apparent dichotomy between explanation and prediction. However, while researchers using PLS-SEM routinely stress the predictive nature of their analyses, model evaluation assessment relies exclusively on metrics designed to assess the path model’s explanatory power. Recent research has proposed PLSpredict, a holdout sample-based procedure that generates case-level predictions on an item or a construct level. This paper offers guidelines for applying PLSpredict and explains the key choices researchers need to make using the procedure.,The authors discuss the need for prediction-oriented model evaluations in PLS-SEM and conceptually explain and further advance the PLSpredict method. In addition, they illustrate the PLSpredict procedure’s use with a tourism marketing model and provide recommendations on how the results should be interpreted. While the focus of the paper is on the PLSpredict procedure, the overarching aim is to encourage the routine prediction-oriented assessment in PLS-SEM analyses.,The paper advances PLSpredict and offers guidance on how to use this prediction-oriented model evaluation approach. Researchers should routinely consider the assessment of the predictive power of their PLS path models. PLSpredict is a useful and straightforward approach to evaluate the out-of-sample predictive capabilities of PLS path models that researchers can apply in their studies.,Future research should seek to extend PLSpredict’s capabilities, for example, by developing more benchmarks for comparing PLS-SEM results and empirically contrasting the earliest antecedent and the direct antecedent approaches to predictive power assessment.,This paper offers clear guidelines for using PLSpredict, which researchers and practitioners should routinely apply as part of their PLS-SEM analyses.,This research substantiates the use of PLSpredict. It provides marketing researchers and practitioners with the knowledge they need to properly assess, report and interpret PLS-SEM results. Thereby, this research contributes to safeguarding the rigor of marketing studies using PLS-SEM.

Predictive model assessment in PLS-SEM: guidelines for using PLSpredict

Introduction. 1. Fractional Programming Applications. 2. Convex, Quasiconvex, Pseudoconvex, Logarithmic Convex, alpham-Convex, and Invex Functions. 3. Methods for Solving Linear Fractional Programming Problems. 4. Nonlinear Fractional Programming. 5. Duality in Fractional Programming. 6. Fractional Programming with Multiple Objective Functions. 7. Fractional Programming in the Complex Space. 8. Special Linear Fractional Programming Problems. 9. Integer and Mixed Integer Linear Fractional Programming. 10. Fractional Transportation Problem. Bibliography. Subject Index. Author Index.

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Fractional Programming: Theory, Methods and Applications

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of prediction accuracy in businesses and organizations. It is, however, biased: when used to select among...

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A better measure of relative prediction accuracy for model selection and model estimation

When using a model for prediction, or for representing the data, the percentage error may be more important than the absolute error. We therefore present the method of least squares regression based on percentage errors. Exact expressions are derived for the coefficients, and we show how models can be estimated easily using existing regression software. (The proposed method is not to be confused with semi-log regression.) Least squares percentage regression is linked to the multiplicative error model in the same way that the standard additive error model is linked to ordinary least squares regression. The method should therefore also prove useful when the data does not have constant variance (heteroscedastic data). The coefficients are shown to be unbiased. When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates.

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Least Squares Percentage Regression

Simple additive weighting is a well-known method for scoring and ranking alternative options based on multiple attributes. However, the pitfalls associated with this approach are not widely appreciated. For example, the apparently innocuous step of normalizing the various attribute data in order to obtain comparable figures leads to markedly different rankings depending on which normalization is chosen. When the criteria are aggregated using multiplication, such difficulties are avoided because normalization is no longer required. This removes an important source of subjectivity in the analysis because the analyst no longer has to make a choice of normalization type. Moreover, it also permits the modelling of more realistic preference behaviour, such as diminishing marginal utility, which simple additive weighting does not provide. The multiplicative approach also has advantages when aggregating the ratings of panel members. This method is not new but has been ignored for too long by both practitioners and teachers. We aim to present it in a nontechnical way and illustrate its use with data on business schools.

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Add or Multiply? A Tutorial on Ranking and Choosing with Multiple Criteria

http://uhra.herts.ac.uk/bitstream/handle/2299/1014/901123.pdf?sequence=1

Chris Tofallis

Papers

Fractional Programming: Theory, Methods and Applications

A better measure of relative prediction accuracy for model selection and model estimation

Least Squares Percentage Regression

Add or Multiply? A Tutorial on Ranking and Choosing with Multiple Criteria

Input efficiency profiling: an application to airlines