ci_bod_constr_bad {Compind} | R Documentation |

## Constrained Benefit of the Doubt approach (BoD) in presence of undesirable indicators

### Description

The 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).

### Usage

`ci_bod_constr_bad(x, indic_col, ngood=1, nbad=1, low_w=0, pref=NULL)`

### Arguments

`x` |
A data.frame containing simple indicators; the order is important: first columns must contain the desirable indicators, while second ones the undesirable 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 |

### Value

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

`ci_bod_constr_bad_est` |
Composite indicator estimated values. |

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

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

`ci_bod_constr_bad_target` |
Indicator target values. |

### Author(s)

Fusco E., Rogge N.

### References

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.

### See Also

### Examples

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

*Compind*version 3.1 Index]