Compind (version 3.2)

normalise_ci: Normalisation and polarity functions

Description

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

Usage

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

Value

ci_norm

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

norm_method

Normalisation method used.

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: $$z_{ij}=z.mean \pm \frac{x_{ij}-M_{x_j}}{S_{x_j}}\cdot z.std$$ 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": $$\frac{x-min(x)}{max(x)-min(x)}$$ if polarity="NEG": $$\frac{max(x)-x}{max(x)-min(x)}$$

• 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".

Author

Vidoli F.

References

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

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)