# Rate of change (RoC) calculation using DEA Employs `dm.dea` over time to calculate RoCs. ```r roc.dea(xdata, ydata, date, t, rts="crs", orientation, sg="ssm", ftype="d", ncv=NULL, env=NULL, cv="convex") ``` ## Arguments - `xdata`: Input(s) vector (**n** by **m**) - `ydata`: Output(s) vector (**n** by **s**) - `date`: Production date (**n** by **1**) - `t`: A vantage point from which the RoC is captured - `rts`: Returns to scale assumption `"crs"`Constant RTS (default) `"vrs"`Variable RTS `"irs"`Increasing RTS `"drs"`Decreasing RTS - `orientation`: Orientation of the measurement `"i"`Input-orientation `"o"`Output-orientation - `sg`: Employs second-stage optimization `"ssm"`Slack-sum maximization (default) `"max"`Date-sum maximization `"min"`Date-sum minimization - `ftype`: Frontier type `"d"`Dynamic frontier (default) `"s"`Static frontier - `ncv`: Non-controllable variable index(binary) for internal NDF (**1** by **(m+s)**) - `env`: Environment index for external NDF (**n** by **1**) - `cv`: Convexity assumption `"convex"`Convexity holds (default) `"fdh"`Free disposal hull (this will override `rts`) ## Returns - **`$eff_r`**: Efficiency at release (i.e., at each production date) - **`$eff_t`**: Efficiency at `t` - **`$lambda_t`**: Intensity vector at `t` - **`$eft_date`**: Effective date - **`$roc_past`**: RoC observed from the obsolete DMUs in the past - **`$roc_avg`**: Average RoC - **`$roc_local`**: Local RoC ## References Lim, Dong-Joon, Timothy R. Anderson, and Oliver Lane Inman. "Choosing effective dates from multiple optima in Technology Forecasting using Data Envelopment Analysis (TFDEA)." **Technological Forecasting and Social Change** 88 (2014): 91~97. Lim, Dong-Joon, et al. "Comparing technological advancement of hybrid electric vehicles (HEV) in different market segments." **Technological Forecasting and Social Change** 97 (2015): 140~153. Lim, Dong-Joon, and Dong-Hyuk Yang. "Assessment of Regulatory Requirements on Technological Changes: The Increasing Dominance of Downsized Turbo/Super-Charged Engines Over Naturally Aspirated Engines." **IEEE Access** 7 (2019): 84839-84848. ## Author(s) Dong-Joon Lim, PhD ## See Also `dm.dea` Distance measure using DEA `roc.dea` RoC calculation using DEA `map.soa.dea` SOA mapping using DEA `target.arrival.dea` Arrival target setting using DEA `target.spec.dea` Spec target setting using DEA ## Examples ```r # Reproduce Table 3 in Lim, D-J. et al.(2014) # Load airplane dataset df <- dataset.airplane.2017 # ready x <- data.frame(Flew = rep(1, 28)) y <- subset(df, select = 3 : 7) d <- subset(df, select = 2) # go roc.dea(x, y, d, 2007, "vrs", "o", "min", "d")$roc_past # Reproduce Table 3 in Lim, D-J. et al.(2015) # Load hev dataset df <- dataset.hev.2013 # ready x <- subset(df, select = 3) y <- subset(df, select = 4 : 6) d <- subset(df, select = 2) c <- subset(df, select = 7) # go results <- roc.dea(x, y, d, 2013, "vrs", "o", "min", "d", env = c) hev <- which(results$roc_local > 0) data.frame(Class = c[hev, ], SOA = hev, LocalRoC = results$roc_local[hev, ])[order(c[hev, ]), ] # NOTE: the published results include a typo on roc_local[82,] # this has been corrected in Lim, D-J. et al. (2016). ```

roc.dea function