pattern.GDM1 {clusterSim}

An application of GDM1 distance for metric data to compute the distances of objects from the pattern object (upper or lower)

Description

An application of GDM1 distance for metric data to compute the distances of objects from the upper (ideal point co-ordinates) or lower (anti-ideal point co-ordinates) pattern object

Usage

pattern.GDM1(data, performanceVariable, scaleType="i",
nomOptValues=NULL, weightsType="equal", weights=NULL,
normalization="n0", patternType="upper",
patternCoordinates="dataBounds", patternManual=NULL,
nominalTransfMethod=NULL)

Arguments

data

matrix or dataset

performanceVariable

vector containing three types of performance variables:

s for stimulants where higher value means better performance

d for destimulants where low values indicate better performance

n for nominants where the best value is implied. Object performance is positively assessed if the measure has implied value

scaleType

"i" - variables measured on interval scale, "r" - variables measured on ratio scale, "r/i" - vector with mixed variables

nomOptValues

vector containing optimal values for nominant variables and NA values for stimulants and destimulants. If performanceVariable do not contain nominant variables this nomOptValues may be set to NULL

weightsType

equal or different1 or different2

"equal" - equal weights

"different1" - vector of different weights should satisfy conditions: each weight takes value from interval [0; 1] and sum of weights equals one

"different2" - vector of different weights should satisfy conditions: each weight takes value from interval [0; m] and sum of weights equals m (m - the number of variables)

normalization

normalization formulas as in data.Normalization function

weights

vector of weights

patternType

"upper" - ideal point co-ordinates consists of the best variables' values

"lower" - anti-ideal point co-ordinates consists of the worst variables' values

patternCoordinates

"dataBounds" - pattern should be calculated as following: "upper" pattern (maximum for stimulants, minimum for destimulants), "lower" pattern (minimum for stimulants, maximum for destimulants)

"manual" - pattern should be given in patternManual variable

patternManual

Pattern co-ordinates contain:

real numbers

"min" - for minimal value of variable

"max" - for maximal value of variable

nominalTransfMethod

method of transformation of nominant to stimulant variable:

"q" - quotient transformation

"d" - difference transformation

Details

See file ../doc/patternGDM1_details.pdf for further details

Value

pdata

raw (primary) data matrix

tdata

data matrix after transformation of nominant variables (with pattern in last row)

data

data matrix after normalization (with pattern in last row)

distances

GDM1 distances from pattern object

sortedDistances

sorted GDM1 distances from pattern object

Author(s)

Marek Walesiak [e-mail], Andrzej Dudek [e-mail]

Department of Econometrics and Computer Science, University of Economics, Wroclaw, Poland

References

Jajuga, K., Walesiak, M., Bak, A. (2003), On the general distance measure, In: M. Schwaiger, O. Opitz (Eds.), Exploratory data analysis in empirical research, Springer-Verlag, Berlin, Heidelberg, 104-109. Available at: doi:10.1007/978-3-642-55721-7_12.

Walesiak, M. (1993), Statystyczna analiza wielowymiarowa w badaniach marketingowych [Multivariate statistical analysis in marketing research]. Wroclaw University of Economics, Research Papers no. 654.

Walesiak, M. (2006), Uogolniona miara odleglosci w statystycznej analizie wielowymiarowej [The Generalized Distance Measure in multivariate statistical analysis], Wydawnictwo AE, Wroclaw.

Walesiak, M. (2011), Uogólniona miara odległości GDM w statystycznej analizie wielowymiarowej z wykorzystaniem programu R [The Generalized Distance Measure GDM in multivariate statistical analysis with R], Wydawnictwo Uniwersytetu Ekonomicznego, Wroclaw.

Walesiak, M. (2016), Uogólniona miara odległości GDM w statystycznej analizie wielowymiarowej z wykorzystaniem programu R. Wydanie 2 poprawione i rozszerzone [The Generalized Distance Measure GDM in multivariate statistical analysis with R], Wydawnictwo Uniwersytetu Ekonomicznego, Wroclaw.

See Also

dist.GDM,data.Normalization

Examples

# Example 1
library(clusterSim)
data(data_patternGDM1)
res<-pattern.GDM1(data_patternGDM1,
performanceVariable=c("s","s","s","s","s","s","d","d","s","s"),
scaleType="r",nomOptValues=NULL,weightsType<-"equal",weights=NULL,
normalization<-"n4",patternType<-"lower",patternCoordinates<-"manual",
patternManual<-c("min","min","min","min","min","min","max","max","min","min"),
nominalTransfMethod <-NULL)
print(res)
gdm_p<-res$distances
plot(cbind(gdm_p,gdm_p),xlim=c(max(gdm_p),min(gdm_p)),
ylim=c(min(gdm_p),max(gdm_p)),xaxt="n",
xlab="Order of objects from the best to the worst", 
ylab="GDM distances from pattern object", lwd=1.6)
axis(1, at=gdm_p,labels=names(gdm_p), cex.axis=0.5)

# Example 2
library(clusterSim)
data(data_patternGDM1)
res<-pattern.GDM1(data_patternGDM1,
performanceVariable=c("s","s","s","s","s","s","d","d","s","s"),
scaleType="r",nomOptValues=NULL,weightsType<-"equal",weights=NULL,
normalization<-"n2",patternType<-"upper",
patternCoordinates<-"dataBounds",patternManual<-NULL,
nominalTransfMethod<-NULL)
print(res)
gdm_p<-res$distances
plot(cbind(gdm_p,gdm_p),xlim=c(min(gdm_p),max(gdm_p)),
ylim=c(min(gdm_p),max(gdm_p)),xaxt="n",
xlab="Order of objects from the best to the worst", 
ylab="GDM distances from pattern object", lwd=1.6)
axis(1, at=gdm_p,labels=names(gdm_p), cex.axis=0.5)

# Example 3
library(clusterSim)
data(data_patternGDM1)
res<-pattern.GDM1(data_patternGDM1,
performanceVariable=c("s","s","s","s","s","s","d","d","s","s"),
scaleType="r",nomOptValues=NULL,weightsType<-"different2",
weights=c(1.1,1.15,1.15,1.1,1.1,0.7,0.7,1.2,0.8,1.0),
normalization<-"n6",patternType<-"upper",patternCoordinates<-"manual",
patternManual<-c(100,100,100,100,100,"max","min","min","max","max"),
nominalTransfMethod <-NULL)
print(res)
gdm_p<-res$distances
plot(cbind(gdm_p,gdm_p),xlim=c(min(gdm_p),max(gdm_p)),
ylim=c(min(gdm_p),max(gdm_p)),xaxt="n",
xlab="Order of objects from the best to the worst", 
ylab="GDM distances from pattern object", lwd=1.6)
axis(1, at=gdm_p,labels=names(gdm_p), cex.axis=0.5)