ci_rbod_constr_bad {Compind} | R Documentation |

The Robust constrained Benefit of the Doubt function introduces additional constraints to the weight variation in the optimization procedure (Constrained Virtual Weights Restriction) allowing to restrict the importance attached to a single indicator expressed in percentage terms, ranging between a lower and an upper bound (VWR); this function, furthermore, allows to calculate the composite indicator simultaneously in presence of undesirable (bad) and desirable (good) indicators allowing to impose a preference structure (ordVWR). This function is the robust version of the `ci_bod_constr_bad`

: it is based on the concept of the expected minimum input function of order-*m* (Daraio and Simar, 2005) allowing to compare the unit under analysis against `M`

peers by extracting `B`

samples with replacement.

`ci_rbod_constr_bad(x, indic_col, ngood=1, nbad=1, low_w=0, pref=NULL, M, B) `

`x` |
A data.frame containing simple indicators. |

`indic_col` |
A numeric list indicating the positions of the simple indicators. |

`ngood` |
The number of desirable outputs; it has to be greater than 0. |

`nbad` |
The number of undesirable outputs; it has to be greater than 0. |

`low_w` |
Importance weights lower bound. |

`pref` |
The preference vector among indicators; For example if |

`M` |
The number of elements in each of the bootstrapped samples. |

`B` |
The number of bootstrap replicates. |

An object of class "CI". This is a list containing the following elements:

`ci_rbod_constr_bad_est` |
Composite indicator estimated values. |

`ci_method` |
Method used; for this function ci_method="rbod_constr_bad". |

`ci_rbod_constr_bad_weights` |
Raw weights assigned to each simple indicator. |

`ci_rbod_constr_bad_target` |
Indicator target values. |

Fusco E., Rogge N.

Rogge N., de Jaeger S. and Lavigne C. (2017) "*Waste Performance of NUTS 2-regions in the EU: A Conditional Directional Distance Benefit-of-the-Doubt Model*", Ecological Economics, vol.139, pp. 19-32.

Zanella A., Camanho A.S. and Dias T.G. (2015) "*Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis*", European Journal of Operational Research, vol. 245(2), pp. 517-530.

`ci_bod_constr`

, `ci_bod_constr_bad`

```
data(EU_2020)
indic <- c("employ_2011", "percGDP_2011", "gasemiss_2011","deprived_2011")
dat <- EU_2020[-c(10,18),indic]
# Robust BoD Constrained VWR
CI_BoD_C = ci_rbod_constr_bad(dat, ngood=2, nbad=2, low_w=0.05, pref=NULL, M=10, B=50)
CI_BoD_C$ci_rbod_constr_bad_est
# Robust BoD Constrained ordVWR
importance <- c("gasemiss_2011","percGDP_2011","employ_2011")
CI_BoD_C = ci_rbod_constr_bad(dat, ngood=2, nbad=2, low_w=0.05, pref=importance, M=10, B=50)
CI_BoD_C$ci_rbod_constr_bad_est
```

[Package *Compind* version 2.8 Index]