DEA 1.0.0

First release.

This package succeeds DEA 0.1-2, published in 2008 by Zuleyka Diaz-Martinez and Jose Fernandez-Menendez and archived shortly afterwards. Both are authors of this package.

The two cover the same ground — the 2008 package had CCR, BCC, additive and slacks-based models in envelopment and multiplier form — but no code is carried over. The 2008 package bundled a C implementation of the simplex method from GLPK; this one has no compiled code at all and solves through lpSolveAPI. The implementation is new throughout and the API is entirely different:

All sixteen entry points of 0.1-2 are covered, envelopment and multiplier form alike. Code written against them will not run: the names, the arguments and the return values are all different. The version number starts at 1.0.0 rather than 0.1.0 because 0.1.0 would rank below the archived 0.1-2 under R’s version ordering.

Prices, and weights

• dea(..., multipliers = TRUE) solves the multiplier (dual) program at each DMU and returns the optimal weights v on the inputs, u on the outputs and the returns-to-scale intercept u0, in the caller’s own units. multipliers(fit) puts them in one matrix. For an efficient DMU these are not unique – there is a whole face of optimal weight vectors – and the documentation says so rather than leaving it to be discovered.

• dea_cost() and dea_revenue() – cost and revenue efficiency, each factoring exactly into technical times allocative, so a DMU that sits on the frontier while buying the wrong mix for its prices is visible as such.

• dea_profit() – Nerlovian profit inefficiency, the profit gap normalized by the value of a direction. It adds into technical plus allocative rather than multiplying, because observed profit is routinely zero or negative and a ratio is undefined exactly where the question matters. Constant and non-decreasing returns are refused: maximum profit over a cone is unbounded as soon as one reference DMU is profitable.

• dea_cross() – cross-efficiency, with the Doyle and Green (1994) benevolent and aggressive secondary goals. Plain cross-efficiency depends on which vertex of an optimal face the solver stopped at, and the spread is first-order rather than numerical; running both goals brackets it. On charnes1981 the constant-returns model calls 19 of 70 sites efficient and cannot rank them, and cross-efficiency ranks all 70 with no ties.

Estimators

• dea() — radial Debreu-Farrell technical efficiency under constant ("crs"), variable ("vrs"), non-increasing ("nirs") and non-decreasing ("ndrs") returns to scale, and under free disposal ("fdh"), in either orientation. Optional second-stage slack maximization, Andersen-Petersen super-efficiency, and an explicit reference technology through xref/yref.

• dea_sbm() — the slacks-based measure of Tone (2001), non-oriented, input-oriented or output-oriented. The non-oriented measure is a fractional program and is solved exactly by the Charnes-Cooper linearization.

• dea_add() — the additive model of Charnes, Cooper, Golany, Seiford and Stutz (1985), with three objective weightings: the Range Adjusted Measure of Cooper, Park and Pastor (1999), the Measure of Inefficiency Proportions, and the original unweighted total. One program on three scales; the projection and the efficient set are identical across them, and that set is exactly the Pareto-Koopmans set dea() and dea_sbm() find.

• dea_ddf() — the directional distance function of Chambers, Chung and Fare (1996), with the direction given as one of five shorthands, a fixed vector, or one row per DMU. Accepts zero and negative data, which the radial and slacks-based measures cannot.

• dea_rts() — scale efficiency and the returns-to-scale classification, from a single sweep of the constant-, variable- and non-increasing-returns technologies.

Inference

• dea_boot() — the smoothed homogeneous bootstrap of Simar and Wilson (1998): bias, bootstrap standard error, bias-corrected efficiency and percentile confidence intervals. Reports Simar and Wilson’s own |bias|/se > 1/sqrt(3) rule per DMU as correct_worthwhile rather than applying the correction silently. Parallel over replications through parallel::mclapply.

• dea_rate() — the rate a DEA estimator can attain, as the slope of log mean squared error on log sample size, given the number of inputs and outputs and the returns-to-scale assumption.

• dea_sim() — simulate a convex, freely disposable technology whose input- and output-oriented Farrell efficiencies have a closed form, so that an estimator can be scored against a truth rather than against another implementation.

Data

• charnes1981 — the Program Follow Through data of Charnes, Cooper and Rhodes (1981), 70 school sites with five inputs and three outputs. The original DEA application, and the standard worked example in the field. Identical to the copies distributed as Benchmarking::charnes1981 and npsf::ccr81, which were checked against each other before this one was made.

Interface

• x and y accept matrices, data frames, bare numeric vectors, or – with data – character column names or one-sided formulas.

• One result class, "dea", shared by all three estimators, with print(), summary(), plot(), fitted(), nobs(), efficiency(), peers() and slacks() methods. efficiency(fit, "score") maps every model’s measure onto a common (0, 1] scale, and deliberately refuses to do so for a directional model whose direction is neither purely input nor purely output, because no such mapping exists.

• "drs" and "irs" are accepted as aliases for "nirs" and "ndrs", the spellings Benchmarking uses, so switching packages does not silently change the model.

• A stray positional argument is refused rather than absorbed. data is the third positional argument of every entry point, so dea_add(x, y, "ram") used to put "ram" there and silently take the default measure. It now errors.

• Input and output columns are rescaled to mean one before solving. Radial efficiency, the slacks-based measure and a proportional-direction directional distance are all invariant to this, so no answer changes and the linear program is much better conditioned; slacks come back in the caller’s own units.