Compind (version 3.2)

ci_ogwa: Ordered Geographically Weighted Average (OWA)

Description

The Ordered Geographically Weighted Averaging (OWA) operator is an extension of the multi-criteria decision aggregation method called OWA (Yager, 1988) that accounts for spatial heterogeneity.

Usage

ci_ogwa(x, id, indic_col, atleastjp, coords,
                    kernel = "bisquare", adaptive = F, bw, 
                    p = 2, theta = 0, longlat = F, dMat)

Value

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

CI_OGWA_n

Composite indicator estimated values for OGWA-.

CI_OGWA_p

Composite indicator estimated values for OGWA+.

wp

OGWA weights' vector "More than j".

wn

OGWA weights' vector "At least j".

ci_method

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

Arguments

x

A data.frame containing score of the simple indicators.

id

Units' unique identifier.

indic_col

Simple indicators column number.

coords

A two-column matrix of latitude and longitude coordinates.

atleastjp

Fuzzy linguistic quantifier "At least j".

kernel

function chosen as follows: gaussian: wgt = exp(-.5*(vdist/bw)^2); exponential: wgt = exp(-vdist/bw); bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise; tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise; boxcar: wgt=1 if dist < bw, wgt=0 otherwise.

adaptive

if TRUE calculate an adaptive kernel where the bandwidth (bw) corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance).

bw

bandwidth used in the weighting function.

p

the power of the Minkowski distance, default is 2, i.e. the Euclidean distance.

theta

an angle in radians to rotate the coordinate system, default is 0.

longlat

if TRUE, great circle distances will be calculated.

dMat

a pre-specified distance matrix, it can be calculated by the function gw.dist.

Author

Fusco E., Liborio M.P.

References

Fusco, E., Liborio, M.P., Rabiei-Dastjerdi, H., Vidoli, F., Brunsdon, C. and Ekel, P.I. (2023), Harnessing Spatial Heterogeneity in Composite Indicators through the Ordered Geographically Weighted Averaging (OGWA) Operator. Geographical Analysis. https://doi.org/10.1111/gean.12384

See Also

ci_owa

Examples

data(data_HPI)

data_HPI_2019 = data_HPI[data_HPI$year==2019,]
Indic_name = c("Life_Expectancy","Ladder_of_life","Ecological_Footprint")

Indic_norm = normalise_ci(data_HPI_2019, Indic_name, c("POS","POS","NEG"),method=2)$ci_norm
Indic_norm = Indic_norm[Indic_norm$Life_Expectancy>0 & 
              Indic_norm$Ladder_of_life>0 & 
              Indic_norm$Ecological_Footprint >0,]

Indic_CI = data.frame(Indic_norm, 
                       data_HPI_2019[rownames(Indic_norm),
                       c("lat","long","HPI","ISO","Country")])

atleast = 2

coord = Indic_CI[,c("lat","long")]

CI_ogwa_n = ci_ogwa(Indic_CI, id="ISO", 
                      indic_col=c(1:3), 
                      atleastjp=atleast,
                      coords=as.matrix(coord),
                      kernel = "gaussian",
                      adaptive=FALSE, 
                      longlat=FALSE)$CI_OGWA_n


#CI_ogwa_p = ci_ogwa(Indic_CI, id="ISO", 
#                      indic_col=c(1:3), 
#                     atleastjp=atleast,
#                      coords=as.matrix(coord),
#                      kernel = "gaussian",
#                      adaptive=FALSE, 
#                      longlat=FALSE)$CI_OGWA_p