tenonradialbc: Statistical Inference Regarding the Russell Measure of...
In npsf: Nonparametric and Stochastic Efficiency and Productivity Analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Routine tenonradialbc performs bias correction of the nonradial Russell input- or output-based measure of technical efficiency, computes bias and constructs confidence intervals via bootstrapping techniques.

 tenonradialbc(formula, data, subset,
            ref = NULL, data.ref = NULL, subset.ref = NULL,
            rts = c("C", "NI", "V"), base = c("output", "input"),
            homogeneous = TRUE, smoothed = TRUE, kappa = NULL,
            reps = 999, level = 95,
            print.level = 1, show.progress = TRUE, seed = NULL)

`formula`	an object of class “formula” (or one that can be coerced to that class): a symbolic description of the model. The details of model specification are given under ‘Details’.
`data`	an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment (`formula`), typically the environment from which `teradial` is called.
`subset`	an optional vector specifying a subset of observations for which technical efficiency is to be computed.
`rts`	character or numeric. string: first letter of the word “c” for constant, “n” for non-increasing, or “v” for variable returns to scale assumption. numeric: 3 for constant, 2 for non-increasing, or 1 for variable returns to scale assumption.
`base`	character or numeric. string: first letter of the word “o” for computing output-based or “i” for computing input-based technical efficiency measure. string: 2 for computing output-based or 1 for computing input-based technical efficiency measure
`ref`	an object of class “formula” (or one that can be coerced to that class): a symbolic description of inputs and outputs that are used to define the technology reference set. The details of technology reference set specification are given under ‘Details’. If reference is not provided, the technical efficiency measures for data points are computed relative to technology based on data points themselves.
`data.ref`	an optional data frame containing the variables in the technology reference set. If not found in `data.ref`, the variables are taken from environment(ref), typically the environment from which `teradial` is called.
`subset.ref`	an optional vector specifying a subset of observations to define the technology reference set.
`smoothed`	logical. If TRUE, the reference set is bootstrapped with smoothing; if FALSE, the reference set is bootstrapped with subsampling.
`homogeneous`	logical. Relevant if `smoothed=TRUE`. If TRUE, the reference set is bootstrapped with homogeneous smoothing; if FALSE, the reference set is bootstrapped with heterogeneous subsampling.
`kappa`	relevant if `smoothed=TRUE`. 'kappa' sets the size of the subsample as K^kappa, where K is the number of data points in the original reference set. The default value is 0.7. 'kappa' may be between 0.5 and 1.
`reps`	specifies the number of bootstrap replications to be performed. The default is 999. The minimum is 100. Adequate estimates of confidence intervals using bias-corrected methods typically require 1,000 or more replications.
`level`	sets confidence level for confidence intervals; default is `level=95`.
`show.progress`	logical. Relevant if `print.level>=1`. If TRUE, progress of the bootstrap is displayed; if FALSE, display of the bootstrap progress is suppressed.
`print.level`	numeric. 0 - nothing is printed; 1 - print summary of the model and data. 2 - print summary of technical efficiency measures. 3 - print estimation results observation by observation. Default is 1.
`seed`	numeric. The seed (for replication purposes).

Models for tenonradialbc are specified symbolically. A typical model has the form outputs ~ inputs, where outputs (inputs) is a series of (numeric) terms which specifies outputs (inputs). The same goes for reference set. Refer to the examples.

Results can be summarized using summary.npsf.

tenonradialbc returns a list of class npsf containing the following elements:

`K`	numeric: number of data points.
`M`	numeric: number of outputs.
`N`	numeric: number of inputs.
`rts`	string: RTS assumption.
`base`	string: base for efficiency measurement.
`reps`	numeric: number of bootstrap replications.
`level`	numeric: confidence level for confidence intervals.
`te`	numeric: radial measure (Russell) of technical efficiency.
`tebc`	numeric: bias-corrected radial measures of technical efficiency.
`biasboot`	numeric: bootstrap bias estimate for the original radial measures of technical efficiency.
`varboot`	numeric: bootstrap variance estimate for the radial measures of technical efficiency.
`biassqvar`	numeric: one-third of the ratio of bias squared to variance for radial measures of technical efficiency.
`realreps`	numeric: actual number of replications used for statistical inference.
`telow`	numeric: lower bound estimate for radial measures of technical efficiency.
`teupp`	numeric: upper bound estimate for radial measures of technical efficiency.
`teboot`	numeric: `reps x K` matrix containing bootstrapped measures of technical efficiency from each of `reps` bootstrap replications.
`esample`	logical: returns TRUE if the observation in user supplied data is in the estimation subsample and FALSE otherwise.

Before specifying option homogeneous it is advised to preform the test of independence (see nptestind). Routine nptestrts may help deciding regarding option rts.

Results can be summarized using summary.npsf.

Oleg Badunenko <oleg.badunenko@brunel.ac.uk>, Pavlo Mozharovskyi <pavlo.mozharovskyi@telecom-paris.fr>

Badunenko, O. and Mozharovskyi, P. (2020), Statistical inference for the Russell measure of technical efficiency, Journal of the Operational Research Society, 713, 517–527, doi: 10.1080/01605682.2019.1599778

Färe, R., Grosskopf, S. and Lovell, C. A. K. (1994), Production Frontiers, Cambridge U.K.: Cambridge University Press, doi: 10.1017/CBO9780511551710

teradial, tenonradial, teradialbc, nptestrts, nptestind, sf

 
 ## Not run: 
  
  data( ccr81 )
  head( ccr81 )
  
  # Subsampling

  t9 <- tenonradialbc(y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, data = ccr81,
                          ref = NULL, data.ref = NULL, subset.ref = NULL,
                          rts = "v", base = "i",
                          homogeneous = FALSE, smoothed = TRUE, kappa = .6,
                          reps = 999, level = 95,
                          print.level = 1, show.progress = TRUE, seed = NULL)
  # display the results

  cbind(te = t9$te, telow = t9$telow, tebc = t9$tebc, teupp = t9$teupp, 
        biasboot = t9$biasboot, varboot = t9$varboot, biassqvar = t9$biassqvar)
  
  # Smoothing

  t10 <- tenonradialbc(y1 + y2 + y3 ~ x1 + x2 + x3 + x4 + x5, data = ccr81,
                          ref = NULL, data.ref = NULL, subset.ref = NULL,
                          rts = "v", base = "i",
                          homogeneous = TRUE, smoothed = TRUE, kappa = .6,
                          reps = 999, level = 95,
                          print.level = 1, show.progress = TRUE, seed = NULL)
  # display the results

  cbind(te = t10$te, telow = t10$telow, tebc = t10$tebc, teupp = t10$teupp, 
        biasboot = t10$biasboot, varboot = t10$varboot, biassqvar = t10$biassqvar)
  
 
## End(Not run)