ci_bod_constr_mpi: Non Compensative Constrained Benefit of the Doubt approach (BoD)

Description

The constrained Benefit of the Doubt function lets to introduce additional constraints to the weight variation in the optimization procedure so that all the weights obtained are greater than a lower value (low_w) and less than an upper value (up_w). In a second step the composite indicator is adjusted by a "penalty" coefficient related to the variability of each unit (see, method of the coefficient of variation penalty - ci_mpi)

Usage

ci_bod_constr_mpi(x,indic_col,up_w,low_w,penalty="POS")

Arguments

A data.frame containing simple indicators.

indic_col

A numeric list indicating the positions of the simple indicators.

up_w

Importance weights upper bound.

low_w

Importance weights lower bound.

penalty

Penalty direction; Use "POS" (default) in case of 'increasing' or 'positive' composite index (e.g., well-being index)), "NEG" in case of 'decreasing' or 'negative' composite index (e.g., poverty index).

Value

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

ci_bod_constr_est_mpi

Constrained composite indicator estimated values.

ci_bod_constr_mpi_pen

Penalized constrained composite indicator estimated values.

ci_bod_constr_mpi_weights

Raw constrained weights (not penalized) assigned to the simple indicators.

ci_method

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

References

Van Puyenbroeck T. and Rogge N. (2017) "Geometric mean quantity index numbers with Benefit-of-the-Doubt weights", European Journal of Operational Research, Volume 256, Issue 3, Pages 1004 - 1014.

De Muro P., Mazziotta M., Pareto A. (2011), "Composite Indices of Development and Poverty: An Application to MDGs", Social Indicators Research, Volume 104, Number 1, pp. 1-18.

Examples

Run this code

# NOT RUN {
data(EU_NUTS1)
data_norm = normalise_ci(EU_NUTS1,
                         c(2:3),
                         c("NEG","POS"),
                         method=1,
                         z.mean=100,
                         z.std=10)

CI = ci_bod_constr_mpi(data_norm$ci_norm,
                   c(1:2),
                   up_w=1,
                   low_w=0.1,
                   penalty="POS")
                   
  
# }