samplesize4surveys (version 4.1.1)

ICC: Intraclass Correlation Coefficient

Description

This function computes the intraclass correlation coefficient.

Usage

ICC(y, cl)

Arguments

y

The variable of interest.

cl

The variable indicating the membership of each element to a specific cluster.

Value

The total sum of squares (TSS), the between sum of squqres (BSS), the within sum of squares (WSS) and the intraclass correlation coefficient.

Details

The intraclass correlation coefficient is defined as: $$\rho = 1- \frac{m}{m-1} \frac{WSS}{TSS}$$ Where \(m\) is the average sample sie of units selected inside each sampled cluster.

References

Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas

See Also

ss4p

Examples

# NOT RUN {
##########################################
# Almost same mean in each cluster       #
#                                        #
# - Heterogeneity within clusters        #
# - Homogeinity between clusters         #
##########################################

# Population size
N <- 100000
# Number of clusters in the population
NI <- 1000
# Number of elements per cluster
N/NI

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- rep(1:NI, length.out=N)

table(cl)
tapply(y, cl, FUN=mean)
boxplot(y~cl)
rho = ICC(y,cl)$ICC
rho


##########################################
# Very different means per cluster       #
#                                        #
# - Heterogeneity between clusters       #
# - Homogeinity within clusters          #
##########################################

# Population size
N <- 100000
# Number of clusters in the population
NI <- 1000
# Number of elements per cluster
N/NI

# The variable of interest
y <- c(1:N)
# The clustering factor
cl <- kronecker(c(1:NI),rep(1,N/NI))

table(cl)
tapply(y, cl, FUN=mean)
boxplot(y~cl)
rho = ICC(y,cl)$ICC
rho

############################
# Example 1 with Lucy data #
############################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
y <- Income
cl <- Zone
ICC(y,cl)

############################
# Example 2 with Lucy data #
############################

data(Lucy)
attach(Lucy)
N <- nrow(Lucy)
y <- as.double(SPAM)
cl <- Zone
ICC(y,cl)
# }