kmo = function( data ){
library(MASS)
X <- cor(as.matrix(data))
iX <- ginv(X)
S2 <- diag(diag((iX^-1)))
AIS <- S2%*%iX%*%S2 # anti-image covariance matrix
IS <- X+AIS-2*S2 # image covariance matrix
Dai <- sqrt(diag(diag(AIS)))
IR <- ginv(Dai)%*%IS%*%ginv(Dai) # image correlation matrix
AIR <- ginv(Dai)%*%AIS%*%ginv(Dai) # anti-image correlation matrix
a <- apply((AIR - diag(diag(AIR)))^2, 2, sum)
AA <- sum(a)
b <- apply((X - diag(nrow(X)))^2, 2, sum)
BB <- sum(b)
MSA <- b/(b+a) # indiv. measures of sampling adequacy
AIR <- AIR-diag(nrow(AIR))+diag(MSA) # Examine the anti-image of the
# correlation matrix. That is the
# negative of the partial correlations,
# partialling out all other variables.
kmo <- BB/(AA+BB) # overall KMO statistic
# Reporting the conclusion
if (kmo >= 0.00 && kmo < 0.50){
test <- 'The KMO test yields a degree of common variance
unacceptable for FA.'
} else if (kmo >= 0.50 && kmo < 0.60){
test <- 'The KMO test yields a degree of common variance miserable.'
} else if (kmo >= 0.60 && kmo < 0.70){
test <- 'The KMO test yields a degree of common variance mediocre.'
} else if (kmo >= 0.70 && kmo < 0.80){
test <- 'The KMO test yields a degree of common variance middling.'
} else if (kmo >= 0.80 && kmo < 0.90){
test <- 'The KMO test yields a degree of common variance meritorious.'
} else {
test <- 'The KMO test yields a degree of common variance marvelous.'
}
ans <- list( overall = kmo,
report = test,
individual = MSA,
AIS = AIS,
AIR = AIR )
return(ans)
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