Odds Ratio Approach Research Articles

An odds-ratio approach for handling proportional and bounded values in data envelopment analysis

An odds-ratio approach for handling proportional and bounded values in data envelopment analysis

An odds-ratio approach for handling proportional and bounded values in data envelopment analysis

The usual assumption in data envelopment analysis (DEA) that all input and output values are unconstrained positive values is not always satisfied, such as when analysing proportions, rates, and percentages bound between 0 and 1 (e.g., defect, graduation, satisfaction, or mortality rates). In such cases, solving standard constant returns-to-scale (CRS) DEA models can produce output target values that exceed their upper bounds (e.g., 130% survival or 210% market penetration). Data constrained on other intervals (e.g., patient satisfaction scores between 1 and 5) present a related problem, where a computed target theoretically can exceed its upper bound. We introduce an odds-ratio transformation for such cases that always produces targets within their given bounds and explore its impact on analysis results (efficiency scores, targets, weights), offering the modeller an alternative for evaluating relative efficiency and setting management goals when variable returns-to-scale (VRS) relationships are not appropriate.

An Odds Ratio Approach for Detecting DDF Under the Nested Logit Modeling Framework

An odds ratio approach (ORA) under the framework of a nested logit model was proposed for evaluating differential distractor functioning (DDF) in multiple-choice items and was compared with an existing ORA developed under the nominal response model. The performances of the two ORAs for detecting DDF were investigated through an extensive simulation study. The impact of model misfit on the performance of each ORA was also examined. To facilitate practical interpretation of each method, effect size measures were obtained and compared. Finally, data from a college-level mathematics placement test were analyzed using the two approaches.

Variations on a Theme

This article presents an expository discussion of the use of odds, odds ratios, and functions of odds ratios as an aid to the interpretation of log-linear parameters. While there have been some previous presentations on the use of odds ratios, this method has never been fully and systematically developed for complex situations, nor have the potential problems of interpretation using odds ratios been discussed. The presentation in this article more fully elaborates the possible modes of drawing contrasts with odds ratios using any of the three common parameterizations of a log-linear model (ANOVA-like, regression-like, and logit). The sampling distribution and the calculation of standard errors for odds ratios are also discussed as are some cautions on the interpretation of odds ratios. A data analysis of unemployment using polytomous variables illustrates the application and interpretation of the odds-ratio approach.