knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 6, fig.height = 4 ) library('adea')
Variable selection in DEA is a question that requires full attention before the results of an analysis can be used in a real case, because its results can be significantly modified depending on the variables included in the model. So, variable selection is a keystone step in each DEA application.
The selection procedure can lead to remove a variable that decision maker could want to keep a variable in the model for political, tactical or any other reason.
But the contribution of that variable will be negligible if nothing is done.
cadea function provides a way force the contribution of a variable to a model be at least a given value.
For more information about loads help of the package about
adea or see [@Fernandez2018] and [@Villanueva2021].
Let's load and have a look at the
tokyo_libraries dataset with
First of all let's do an
adea with the following call
input <- tokyo_libraries[, 1:4] output <- tokyo_libraries[, 5:6] m <- adea(input, output) summary(m)
It shows that
Area.I1 has a load under 0.6, which means its contribution to DEA model is negligible.
With the following call to
cadea the contribution of
Area.I1 is force to be higher than 0.6:
mc <- cadea(input, output, load.min = 0.6, load.max = 4) summary(mc)
Note that the maximum value of a variable load is the maximum number of variables of its types, so
load.max = 4 has no effect on results.
Now load level raises to the given value of 0.6, efficiency average decreases a little.
To compare both efficiency set, observe that Spearman correlation coefficient between them is
r round(cor(m$eff, mc$eff, method = 'spearman'), 4).
This can also be seen in the next plot:
plot(m$eff, mc$eff, main ='Initial efficiencies vs constrained model efficiencies')
All these mean that in this case the change are small.
Bigger change can be expected if
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