Specifying Weight Restriction Limits in Data Envelopment Analysis With the Wong and Beasley and Cone Ratio Methods

Abstract

This study presents a new approach for the definition of weight restrictions in Data Envelopment Analysis (DEA) for the one output, multiple inputs case, using the results of a Linear Regression model (LRM) developed with the same DEA variables. Thus, the limits of Wong-Beasley and Cone Ratio methods are chosen without interference from a decision maker, with DEA weight search intervals defined from the estimated standardized coefficients of a linear regression (which represent the statistical importance of the inputs for the definition of the DEA efficiency scores). As an example, weight restrictions for a DEA model (Constant Returns to Scale (CRS)) were obtained through the unrestricted, Wong-Beasley and Cone Ratio methods applied to a dataset consisting of hospital admissions (output), number of beds and number of health professionals (inputs) in the year 2016; and rankings were compared by a Spearman correlation procedure. The regression model had R 2 = 0.89 with coefficients 0.43 (professionals) and 0.54 (beds); and the Spearman correlation among rankings was at least R 2 S = 0.84. In conclusion, rankings were consistent and interpretable, and the approach circumvents the need for a subjective intervention by a decision maker when defining weight restrictions in DEA.

Data Envelopment Analysis (DEA) in health: a literary review of Latin America

“…Given this context, it is essential to acknowledge several studies in the survey lack discussions on the limitations and suggestions for future research. For instance, the discussion of limitations and proposals for improvement through future research were absent in studies such as Lins et al (2007), Gonçalves et al (2007), García Fariñas et al (2007), Salvador-Carulla et al (2008), Cesconetto et al (2008, Pitta (2008), Faria et al (2008), Fonseca and Ferreira (2009), Navarro España and Maza Ávila (2011), Scaratti and Calvo (2012), Iñiguez et al (2012), Santelices et al (2013), Costa et al (2014), Gramani (2014), García Fariñas and García Tapia (2016), Macrini et al (2018), Soares et al (2017), Lins et al (2019), andAbolghasem et al (2019).…”

“…discuss the possibilities and limitations of comparative evaluation of performance related to public spending and the influence of the federative structure, specifically within the scope of the Brazilian Public Healthcare system. In a distinct approach,Macrini et al (2018) focus their analysis on weights.Comparisons across different aspects of health are also made, such as Mendoza-Mendoza et al (2019) comparing efficiency among Latin American countries (Argentina, Brazil, Cuba, Mexico, and Uruguay) in the context of vaccination Salvador-Carulla et al (2008). extend this comparison beyond Latin America, drawing parallels between Chile and Spain in the context of mental health.…”