normalise_ci function

Normalisation and polarity functions

This function lets to normalise simple indicators according to the polarity of each one.

normalise_ci(x, indic_col, polarity, method=1, z.mean=0, z.std=1, ties.method ="average")

Arguments

• x: A data frame containing simple indicators.

• indic_col: Simple indicators column number.

• method: Normalisation methods:

  • 1 (default) = standardization or z-scores using the following formulation:

where $\pm$ depends on polarity parameter and z.mean and z.std represent the shifting parameters. * 2 = Min-max method using the following formulation:

   if **polarity**="POS": 

   if **polarity**="NEG": 

 * 3 = Ranking method. If **polarity**="POS" ranking is increasing, while if **polarity**="NEG" ranking is decreasing. 

• polarity: Polarity vector: "POS" = positive, "NEG" = negative. The polarity of a individual indicator is the sign of the relationship between the indicator and the phenomenon to be measured (e.g., in a well-being index, "GDP per capita" has 'positive' polarity and "Unemployment rate" has 'negative' polarity).
• z.mean: If method=1, Average shifting parameter. Default is 0.
• z.std: If method=1, Standard deviation expansion parameter. Default is 1.
• ties.method: If method=3, A character string specifying how ties are treated, see rank for details. Default is "average".

Returns

• ci_norm: A data.frame containing normalised score of the choosen simple indicators.

• norm_method: Normalisation method used.

References

OECD, "Handbook on constructing composite indicators: methodology and user guide", 2008, pag.30.

Author(s)

Vidoli F.

See Also

ci_bod, ci_mpi

Examples

data(EU_NUTS1)

# Standard z-scores normalisation #
data_norm = normalise_ci(EU_NUTS1,c(2:3),c("NEG","POS"),method=1,z.mean=0, z.std=1)
summary(data_norm$ci_norm)

# Normalisation for MPI index #
data_norm = normalise_ci(EU_NUTS1,c(2:3),c("NEG","POS"),method=1,z.mean=100, z.std=10)
summary(data_norm$ci_norm)

data_norm = normalise_ci(EU_NUTS1,c(2:3),c("NEG","POS"),method=2)
summary(data_norm$ci_norm)