| ICLUST.cluster {psych} | R Documentation |
The guts of the ICLUST algorithm. Called by ICLUST.
ICLUST.cluster(r.mat, ICLUST.options)
r.mat |
A correlation matrix |
ICLUST.options |
A list of options (see ICLUST) |
See ICLUST
A list of cluster statistics, described more fully in ICLUST
comp1 |
Description of 'comp1' |
comp2 |
Description of 'comp2' |
...
Although the main code for ICLUST is here in ICLUST.cluster, the more extensive documentation is for ICLUST.
William Revelle
Department of Psychology
Northwestern University
Evanston, Illinois
revelle@northwestern.edu
http://personality-project.org/revelle.html
Revelle, W. 1979, Hierarchical Cluster Analysis and the Internal Structure of Tests. Multivariate Behavioral Research, 14, 57-74.
http://personality-project.org/revelle/publications/iclust.pdf
See also more extensive documentation at
http://personality-project.org/r/r.ICLUST.html
ICLUST.graph,ICLUST, cluster.fit , VSS, omega
## The function is currently defined as
function (r.mat,ICLUST.options) {#should allow for raw data, correlation or covariances
#options: alpha =1 (minimum alpha) 2 (average alpha) 3 (maximum alpha)
# beta =1 (minimum beta) 2 (average beta) 3 (maximum beta)
# correct for reliability
# reverse score items if negative correlations
# stop clustering if beta for new clusters < beta.min
# output =1 (short) 2 (show steps) 3 show rejects as we go
#initialize various arrays and get ready for the first pass
output <- ICLUST.options$output
num.var <- nrow(r.mat)
keep.clustering <- TRUE #used to determine when we are finished clustering
results <- data.frame(matrix(rep(0,18*(num.var-1)),ncol=18))
names(results) <- c("Item/Cluster", "Item/Cluster","similarity","correlation","alpha1","alpha2","beta1",
"beta2","size1","size2","rbar1","rbar2","r1","r2","alpha","beta","rbar","size")
rownames(results) <- paste("C",1:(num.var-1),sep="")
clusters <- diag(1,nrow =nrow(r.mat)) #original cluster structure is 1 item clusters
rownames(clusters) <- rownames(r.mat)
colnames(clusters) <- paste("V",1:num.var,sep="")
count=1
#master loop
while (keep.clustering) { #loop until we figure out we should stop
#find similiarities
cluster.stats <- cluster.cor(clusters,r.mat,FALSE) #we will do most of the work on a copy of the r.mat
sim.mat <- cluster.stats$cor #the correlation matrix
diag(sim.mat) <- 0 #we don't want 1's on the diagonal to mess up the maximum
#two ways to estimate reliability -- for 1 item clusters, max correlation, for >1, alpha
#this use of initial max should be an option
if (ICLUST.options$correct) {
row.range <- apply(sim.mat,1,range,na.rm=TRUE) #find the largest and smallest similarities for each variable
row.max <- pmax(abs(row.range[1,]),abs(row.range[2,])) #find the largest absolute similarity
} else {row.max <- rep(1, nrow(sim)) } #don't correct for largest similarity
item.rel <- cluster.stats$alpha
for (i in 1: length(item.rel)) { if (cluster.stats$size[i]<2) {
item.rel[i] <- row.max[i]
#figure out item betas here?
}}
sq.max <- diag(1/sqrt(item.rel)) #used to correct for reliabilities
if (ICLUST.options$correct) {sim <- sq.max
} else {sim <- sim.mat} #this is the corrected for maximum r similarities
diag(sim) <- NA #we need to not consider the diagonal when looking for maxima
#find the most similar pair and apply tests if we should combine
test.alpha <- FALSE
test.beta <- FALSE
while(!(test.alpha&test.beta)){
max.cell <- which.max(sim) #global maximum
if (length(max.cell) < 1) {
keep.clustering <- FALSE
break} #there are no non-NA values left
sign.max <- 1
if ( ICLUST.options$reverse ) { #normal case is to reflect if necessary
min.cell <- which.min(sim) #location of global minimum
if (sim[max.cell] < abs(sim[min.cell] )) {
sign.max <- -1
max.cell <- min.cell }
if (sim[max.cell] < 0.0) {sign.max <- -1 }} #this is a weird case where all the similarities are negative
max.col <- trunc(max.cell/nrow(sim))+1 #is in which row and column?
max.row <- max.cell - (max.col-1)*nrow(sim) #need to fix the case of first column
if (max.row < 1) {max.row <- nrow(sim)
max.col <- max.col-1 }
#combine these two rows if the various criterion are passed
beta.combined <- 2* sign.max*sim.mat[max.cell]/(1+sign.max* sim.mat[max.cell]) #unweighted beta
size1 <- cluster.stats$size[max.row]
if(size1 < 2) {V1 <- 1
beta1 <- item.rel[max.row]
alpha1 <- item.rel[max.row]
rbar1 <- item.rel[max.row] } else {
rbar1 <- results[cluster.names[max.row],"rbar"]
beta1 <- results[cluster.names[max.row],"beta"]
alpha1 <- results[cluster.names[max.row],"alpha"]}
V1 <- size1 + size1*(size1-1) * rbar1
size2 <- cluster.stats$size[max.col]
if(size2 < 2) {V2 <- 1
beta2 <- item.rel[max.col]
alpha2 <- item.rel[max.col]
rbar2 <- item.rel[max.col] } else {
rbar2 <- results[cluster.names[max.col],"rbar"]
beta2 <- results[cluster.names[max.col],"beta"]
alpha2 <- results[cluster.names[max.col],"alpha"]}
V2 <- size2 + size2 * (size2-1) * rbar2
Cov12 <- sign.max* sim.mat[max.cell] * sqrt(V1*V2)
V12 <- V1 + V2 + 2 * Cov12
size12 <- size1 + size2
alpha <- (V12 - size12)*(size12/(size12-1))/V12
rbar <- alpha/(size12-alpha*(size12-1))
#what is the correlation of this new cluster with the two subclusters?
#this considers item overlap problems
c1 <- sign.max*rbar1*size1*size1 + sign.max* Cov12 #corrects for item overlap
c2 <- rbar2*size2*size2 + Cov12 #only flip one of the two correlations with the combined cluster
if(size1 > size2) {r1 <- c1/sqrt(V1*V12)
r2 <- sign.max* c2/sqrt(V2*V12) } else {r1 <-sign.max* c1/sqrt(V1*V12) #flip the smaller of the two clusters
r2 <- c2/sqrt(V2*V12) }
#test if we should combine these two clusters
#first, does alpha increase?
test.alpha <- TRUE
if (ICLUST.options$alpha.size < min(size1,size2)) {
switch(ICLUST.options$alpha, {if (alpha < min(alpha1,alpha2)) {if (output>2) {print(paste ('do not combine ',
cluster.names[max.row],"with", cluster.names[max.col],'new alpha =', round (alpha,2),
'old alpha1 =',round( alpha1,2),"old alpha2 =",round(alpha2,2)))}
test.alpha <- FALSE }},
{if (alpha < mean(alpha1,alpha2)) {if (output>2) {print(paste ('do not combine ', cluster.names[max.row],
"with", cluster.names[max.col],'new alpha =', round (alpha,2),'old alpha1 =',
round( alpha1,2),"old alpha2 =",round(alpha2,2)))}
test.alpha <- FALSE }},
{if (alpha < max(alpha1,alpha2)) {if (output>2) {print(paste ('do not combine ', cluster.names[max.row],
"with", cluster.names[max.col],'new alpha =', round (alpha,2),'old alpha1 =',
round( alpha1,2),"old alpha2 =",round(alpha2,2)))}
test.alpha <- FALSE }}) #end switch
} #end if options$alpha.size
#second, does beta increase ?
test.beta <- TRUE
if (ICLUST.options$beta.size < min(size1,size2)) {
switch(ICLUST.options$beta, {if (beta.combined < min(beta1,beta2)) {if (output>2) {print(
paste ('do not combine ', cluster.names[max.row],"with", cluster.names[max.col],'new beta =',
round (beta.combined,2),'old beta1 =',round( beta1,2),"old beta2 =",round(beta2,2)))}
test.beta <- FALSE }},
{if (beta.combined < mean(beta1,beta2)) {if (output>2) {print(paste ('do not combine ', cluster.names[max.row],
"with", cluster.names[max.col],'new beta =', round (beta.combined,2),'old beta1 =',round( beta1,2),"old beta2 =",round(beta2,2)))}
test.beta <- FALSE }},
{if (beta.combined < max(beta1,beta2)) {if (output>2) {print(paste ('do not combine ', cluster.names[max.row],
"with", cluster.names[max.col],'new beta =', round (beta.combined,2),'old beta1 =',round( beta1,2),"old beta2 =",round(beta2,2)))}
test.beta <- FALSE }}) #end switch
} #end if options$beta.size
if(test.beta&test.alpha) {break } else {
if (beta.combined < ICLUST.options$beta.min) {
keep.clustering <- FALSE #the most similiar pair is not very similar, we should quit
break} else {sim[max.row,max.col] <- NA
sim[max.col,max.row] <- NA }
} #end of test.beta&test.alpha
} #end of while test.alpha&test.beta.loop
#combine and summarize
if (keep.clustering)
{ # we have based the alpha and beta tests, now combine these two variables
clusters[,max.row] <- clusters[,max.row] + sign.max * clusters[,max.col]
cluster.names <- colnames(clusters)
#summarize the results
results[count,1] <- cluster.names[max.row]
results[count,2] <- cluster.names[max.col]
results[count,"similarity"] <- sim[max.cell]
results[count,"correlation"] <- sim.mat[max.cell]
results[count,"alpha1"] <- item.rel[max.row]
results[count,"alpha2"] <- item.rel[max.col]
size1 <- cluster.stats$size[max.row]
size2 <- cluster.stats$size[max.col]
results[count,"size1"] <- size1
results[count,"size2"] <- size2
results[count,"beta1"] <- beta1
results[count,"beta2"] <- beta2
results[count,"rbar1"] <- rbar1
results[count,"rbar2"] <- rbar2
results[count,"r1"] <- r1
results[count,"r2"] <- r2
results[count,"beta"] <- beta.combined
results[count,'alpha'] <- alpha
results[count,'rbar'] <- rbar
results[count,"size"] <- size12
results[count,3:18] <- round(results[count,3:18],ICLUST.options$digits)
#update
cluster.names[max.row] <- paste("C",count,sep="")
colnames(clusters) <- cluster.names
clusters <- clusters[,-max.col]
cluster.names<- colnames(clusters)
#row.max <- row.max[-max.col]
} #end of combine section
if(output > 1) print(results[count,],digits=2)
count=count+1
if ((num.var - count) < ICLUST.options$n.clus) {keep.clustering <- FALSE}
if(num.var - count < 1) {keep.clustering <- FALSE} #only one cluster left
} #end of keep clustering loop
ICLUST.cluster <- list(results=results,clusters=clusters,number <- num.var - count)
} # end ICLUST.cluster