ci_rbod_constr_Q: Conditional robust constrained Benefit of the Doubt approach (BoD)

Description

The Conditional 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 allowing to impose a preference structure (ordVWR). This function, in addition to being robust against outlier data (see ci_rbod_constr_bad function) allows to take into account external contextual continuous (Q) or/and ordinal (Q_ord) variables.

Usage

ci_rbod_constr_Q(x, indic_col, 
low_w=0, pref=NULL, M, B, Q=NULL, Q_ord=NULL, bandwidth)

Arguments

A data.frame containing simple indicators.

indic_col

A numeric list indicating the positions of the simple indicators.

low_w

Importance weights lower bound.

pref

The preference vector among indicators; For example if Indic1 is the most important, Indic2,Indic3 are more important than Indic4 and no preference judgment on Indic5 (= not included in the vector), the pref vector can be written as: c("Indic1", "Indic2","Indic3","Indic4")

The number of elements in each of the bootstrapped samples.

The number of bootstrap replicates.

A matrix containing continuous exogenous variables.

Q_ord

A matrix containing discrete exogenous variables.

bandwidth

Multivariate mixed bandwidth for exogenous variables; it can be calculated by bandwidth_CI function.

Value

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

ci_rbod_constr_Q_est

Composite indicator estimated values.

ci_method

Method used; for this function ci_method="rbod_constr_Q".

ci_rbod_constr_Q_weights

Raw weights assigned to each simple indicator.

ci_rbod_constr_Q_target

Indicator target values.

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.

Examples

Run this code

# NOT RUN {
data(EU_2020)

indic <- c("employ_2011", "gasemiss_2011","deprived_2011")  
dat   <- EU_2020[-c(10,18),indic]
Q_GDP <- EU_2020[-c(10,18),"percGDP_2011"]

# Conditional robust BoD Constrained VWR
band = bandwidth_CI_bad(dat, ngood=1, nbad=2, Q = Q_GDP)

CI_BoD_C = ci_rbod_constr_Q(dat, 
                                low_w=0.05, 
                                pref=NULL, 
                                M=10, 
                                B=50, 
                                Q=Q_GDP, 
                                bandwidth = band$bandwidth)
CI_BoD_C$ci_rbod_constr_Q_est

# }