I recommend you to read the book which mentioned below. The radial models of DEA combine multiple inputs and outputs, the package in R namely "Benchmarking" simulation codes also combine inputs and outputs for single matrix variable. The mentioned book has a topic in which group differences between different input output combination and efficiency measurement is provided.

Follow the link for book👇

https://www.springer.com/gp/book/9781441979605

Dear Anup Kumar Yadava;

I will immediately read the book which you have mentioned. Thanks.

Dear Anup Kumar Yadava ;

In which chapter is the topic that you mentioned? I can't find it. Excuse me.

Dear Alexandru Szel

Excuse me, I don't understand. Please, can you tell me more clearly?

Dear all;

I think I have found something. But I have been still reading.

Cook and Imanirad (2011) suggested that input/output bundles.

Please see;

Cook and Imanirad (2011). "Data Envelopment Analysis in the Presence of Partial Input-to-Output Impacts"

Aydın Özdemir see page no. 156 onward in that book for group differences, production set differences.

Anup Kumar Yadava thanks. I shall immediately read it.

Anup Kumar Yadava

methinks I have mispresented my question. The issue that I have confused;

Suppose that;

Inputs:

a1

a2

a3

b1

b2

b3

I want to combine (a1, a2, a3) as input "a"

I want to combine (b1, b2, b2) as input "b"

Is this possible?

This problem can be solved by using two set of production technology difference in DEA, first you run DEA model with a1, a2,a3 and b1, b2,b3 and list the efficiency scores, then run second DEA model with adding all inputs in single input and all outputs in single outputs and calculate DEA eff scores, now test group differences between these two different efficiency scores, if there is no different then it is fine. Usually for DMUs and Input output minimum requirements criteria we add variables but if you think adding different input output variables will not affect the basic assumptions (separately) of variables then go ahead, for technical efficiency it is ok but may differ for cost efficiency and allocative efficiency models.

Following paper may help you 👇

https://link.springer.com/chapter/10.1007/978-0-387-71607-7_17

Anup Kumar Yadava thanks. This is a good idea. But how can I add all inputs to single input?

There is a little bit confusion here, if you add all inputs and generate a single input, will that single input will represent a combination of all these inputs or not? Suppose there are two types of labour inputs (hired & family labour) I add them and make a single input labour_total (simply by adding two variables set in excel or in R), so theoretically it will be justified in results. I don't know which types of variables you want to add, you have some strong theoretical background regarding that & it should be reasonable.

Maybe PCA-DEA model can solve this issue.

Adler N. and Yazhemsky E. (2010). “Improving discrimination in Data Envelopment Analysis: PCA-DEA or Variable Reduction”, European Journal of Operational Research, 202 (1), pp. 273-284.

Yes, PCA-DEA will definitely help.

Anup Kumar Yadava

For example, According to Agency for Healthcare Research and Quality:

There are 91 Inpatient Quality Indicators. Suppose that I want to use all of them as single input namely Inpatient Quality.

Inpatient Quality Indicators ■ IQI 01 - Esophageal resection volume ■ IQI 02 - Pancreatic resection volume ■ IQI 04 - Abdominal aortic aneurysm (AAA) repair volume ■ IQI 05 - Coronary artery bypass graft (CABG) volume ■ IQI 06 - Percutaneous coronary intervention (PCI) volume ■ IQI 07 - Carotid endarterectomy volume ■ IQI 08 - Esophageal resection mortality rate ■ IQI 09 - Pancreatic resection mortality rate ■ IQI 11 - Abdominal aortic aneurysm repair (AAA) mortality rate ■ IQI 12 - Coronary artery bypass graft (CABG) mortality rate ■ IQI 13 - Craniotomy mortality rate ■ IQI 14 - Hip replacement mortality rate ■ IQI 15 - Acute myocardial infarction (AMI) mortality rate ■ IQI 16 - Heart failure mortality rate ■ IQI 17 - Acute stroke mortality rate ■ IQI 18 - Gastrointestinal hemorrhage mortality ■ IQI 19 - Hip fracture mortality rate ■ IQI 20 - Pneumonia mortality rate ■ IQI 21 - Cesarean delivery rate, uncomplicated ■ IQI 22 - Vaginal birth after cesarean (VBAC) delivery rate, uncomplicated ■ IQI 23 - Laparoscopic cholecystectomy rate ■ IQI 24 - Incidental appendectomy in the elderly rate ■ IQI 25 - Bilateral cardiac catheterization rate ■ IQI 26 - Coronary artery bypass graft (CABG) rate ■ IQI 27 - Percutaneous coronary intervention (PCI) rate ■ IQI 28 - Hysterectomy rate ■ IQI 29 - Laminectomy or spinal fusion rate ■ IQI 30 - Percutaneous coronary intervention (PCI) mortality rate ■ IQI 31 - Carotid endarterectomy mortality rate ■ IQI 32 - Acute myocardial infarction (AMI) mortality rate, without transfer cases ■ IQI 33 - Primary cesarean delivery rate, uncomplicated ■ IQI 34 - Vaginal birth after cesarean (VBAC) rate, all ■ IQI 90 - Mortality for Selected Procedures ■ IQI 91 - Mortality for Selected Conditions

Source:

https://www.qualityindicators.ahrq.gov/Modules/iqi_resources.aspx

https://www.qualityindicators.ahrq.gov/Downloads/Modules/IQI/V50/IQI_Brochure.pdf

These are two many variables, adding them as a single variable I don't think a good choice, Do pca for your model specification. I am also looking forward to this question.

I will try to do PCA-DEA as soon as possible. And I will share the results of PCA-DEA on this topic.

How was your experience with PCA-DEA?. I think for reducing the number of variables it´s a good idea, you will have in only one component the representation of the rest of variables.

Dear Mónica Yuleni Castro-Peña I will try to do PCA-DEA using Adler and Yazhemsky's PCA-DEA (https://nicoleadler.huji.ac.il/pca-dea-program)

Aydın Özdemir thanks for the link :) it can be useful for the future works. I will be attentive to your experience.

Mónica Yuleni Castro-Peña you're welcome. All the best.

Alexandru Szel

Dear all, well, how can i use grey DEA in order to get the inputs/outputs in the same measurement units during PCA-DEA?

Or another question, before conducting PCA-DEA, I should get the inputs/outputs in the same measurement units. But, how can I do?

Do inputs/outputs have to be in the same units of measure in PCA-DEA?

Hi, please check our paper:

https://www.sciencedirect.com/science/article/abs/pii/S0038012120308326

Article A novel method for computing single output for DEA with appl...