Hi all, I have run DEA using DEAP.
I have selected output orientation, and CRS
Some of the peer weights in my results are coming up as greater than 1.
I thought the peer weight represented the mix of DMU's that added up to 1 that the current DMU can follow.
Can someone please explain what this means, I am having no luck looking for academic references to this?
Hi Peta, maybe these two discussions will help you:
https://www.researchgate.net/post/In_Output_oriented_DEA_model_can_efficiency_score_greater_than_one
https://www.researchgate.net/post/Can_someone_explain_the_efficiency_scores_in_the_output_oriented_DEA_models
Best, Dominic
As Magnus Richter noticed this is the case only in BCC-VRS model (under VRS assumption).
This is the structural difference between the Production Possibility Sets (PPS) of CRS and VRS models. These models are accompanied by a certain assumption concerning the returns-to-scale (RTS). The RTS describe the environment in which the DMUs operate, i.e. the RTS indicate for each DMU the relation between a proportional change in inputs and the resulting change in outputs. Under CRS assumption a proportional increase in input levels results in an equiproportionate increase in the output levels. If this assumption does not hold, then the DMUs operate under VRS.
The variable returns to scale assumption is mathematically represented in the envelopment form of the BCC-VRS model by imposing the constraint Σλ=1 . In this way, we demand the projection of each inefficient DMU onto the efficient frontier to be derived as a convex combination of the intensity variables (you call them peer weights) of the peer group (λ > 0) and their corresponding input-output values. On the other hand, under CRS assumption the projections of each inefficient DMU derive in a similar manner but we allow the combination to be only linear (conical to be precise, since we demand only λ>=0).
Therefore, under CRS assumption, if the model proposes for the inefficient DMU A to mimic exactly the efficient DMU B, then λΒ=1, every other λ=0 and the DMU A will be exactly projected onto DMU B on the frontier.
On the contrary, if the model decides that the projection of DMU A should be composed of a lower (greater) level mix of the input-output mix of DMU B, then λΒ1) and the DMU A will be projected on the left (right) of the DMU B onto the frontier.
Finally, from the above we conclude that in CCR-CRS the data are enveloped by a conical hull, while in BCC-VRS the data are enveloped by a convex hull.
Im also facing the same problem. mainly it occurs when we have only a single peer. the problem persists despite the fact that in the output oriented model we restrict the summation of lambda=1.
The solution to this problem lies in the fact that we need to compute the peers and lambda values shortly after solving for theta or phi whichever we assign to the inputs and output sides of the model. this step is between the theta value and the efficiency score which is equal to 1/theta in case of output oriented model.
after trying this method i was successful in obtaining the summation of lambdas equal to 1.
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