A DEA score is a distance to a frontier, and the frontier is built from peers. `psdea» makes the peer set an argument. The weight matrix is used only through its non-zero pattern: a non-zero off-diagonal entry means that the column unit may enter the frontier of the row unit, and the unit itself is always included.
Three units use one unit of input and produce 1, 2 and 4 units of output.
library(psdea)
X <- matrix(c(1, 1, 1), nrow = 1)
Y <- matrix(c(1, 2, 4), nrow = 1)
round(psdea_sbm(X, Y)$eff, 4)## [1] 0.25 0.50 1.00The scores are the ratio to the best observed ratio, 4. Restricting unit 1 to units 1 and 2 lowers the best ratio to 2:
W <- matrix(c(0, 1, 0,
1, 0, 1,
0, 1, 0), 3, 3, byrow = TRUE)
round(psdea_sbm(X, Y, W = W)$eff_loc, 4)## [1] 0.5 0.5 1.0data(psdea_china_energy)
d <- subset(psdea_china_energy, year == 2015 & code <= 8)
W <- psdea_w_contiguity[1:8, 1:8]
fit <- psdea_panel(d, "gdp_real", c("capital", "energy"), "year",
id = "code", bad = "co2", W = W)
fit##
## Reference-set DEA
## observations : 8
## returns : crs
## mean eff (unrestricted): 0.6041
## mean eff (restricted) : 0.8547
## mean gap ratio : 0.7135
## mean local share : 0.3539
## units on the frontier : 2The two shares decompose the shortfall, and they are missing on the frontier because the denominator is zero there:
##
## Reference-set DEA
## observations : 8
## returns :
## mean eff (unrestricted): 0.6041
## mean eff (restricted) : 0.8547## Warning in mean.default(x$tgr, na.rm = TRUE): argument is not numeric or
## logical: returning NA## mean gap ratio : NA
## mean local share : 0.3539
## units on the frontier : 2When the analyst has no prior on who the peers are, the matrix can be built by sparse non-negative reconstruction of each unit’s bundle:
Wl <- psdea_learn_data(d, c("capital", "energy", "gdp_real"), lambda = 0.05, by = "year")
attr(Wl, "n_peers")## [1] 2fit_l <- psdea_panel(d, "gdp_real", c("capital", "energy"), "year",
id = "code", bad = "co2", W = Wl)
mean(fit_l$tgr, na.rm = TRUE)## [1] 0.7712359