# normalise_ci: Normalisation and polarity functions In Compind: Composite Indicators Functions

## Description

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

## Usage

 1 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: 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".

## Value

 ci_norm A data.frame containing normalised score of the choosen simple indicators. norm_method Normalisation method used.

Vidoli F.

## References

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

ci_bod, ci_mpi

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 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) 

### Example output

Loading required package: Benchmarking

Attaching package: 'boot'

The following object is masked from 'package:psych':

logit

Min.   :-2.7432   Min.   :-0.63920
1st Qu.:-0.1263   1st Qu.:-0.45429
Median : 0.3252   Median :-0.31098
Mean   : 0.0000   Mean   : 0.00000
3rd Qu.: 0.6281   3rd Qu.:-0.05248
Max.   : 1.3356   Max.   : 4.30715
Min.   : 72.57   Min.   : 93.61
1st Qu.: 98.74   1st Qu.: 95.46
Median :103.25   Median : 96.89
Mean   :100.00   Mean   :100.00
3rd Qu.:106.28   3rd Qu.: 99.48
Max.   :113.36   Max.   :143.07