[R] KMO sampling adequacy and SPSS -- partial solution
G. Jay Kerns
gkerns at ysu.edu
Mon Aug 6 19:37:11 CEST 2007
Hello,
This is in response to a post from a couple of years back regarding
Kaiser-Meyer-Olkin Measures of Sampling Adequacy.
(http://tolstoy.newcastle.edu.au/R/help/05/12/17233.html)
As it turns out, last year Trujillo-Ortiz et al. at the Universidad
Autonoma de Baja California wrote and posted a script for MATLAB that
does the job. You can see it (with a discussion of KMO statistics) at
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=12736
Please see their post for documentation/citations/references, etc.
I translated the code into R-speak and added a little to the output;
the function and an example are copied below. You can just copy/paste
to the console to try it out, provided you have the MASS package.
Cheers,
Jay
***************************************************
G. Jay Kerns, Ph.D.
Assistant Professor / Statistics Coordinator
Department of Mathematics & Statistics
Youngstown State University
Youngstown, OH 44555-0002 USA
Office: 1035 Cushwa Hall
Phone: (330) 941-3310 Office (voice mail)
-3302 Department
-3170 FAX
E-mail: gkerns at ysu.edu
http://www.cc.ysu.edu/~gjkerns/
# KMO Kaiser-Meyer-Olkin Measure of Sampling Adequacy
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)
} # end of kmo()
# Try Trujillo-Ortiz et al. example
X = scan()
4 1 4 5 2 3 6 7
4 2 7 6 6 3 3 4
6 4 3 4 2 5 7 7
5 3 5 4 3 4 6 7
5 2 4 5 2 5 5 6
6 3 3 5 4 4 7 7
6 2 4 4 4 3 4 5
4 1 3 4 3 3 5 6
5 3 4 3 4 3 6 6
5 4 3 4 4 4 6 7
6 2 4 4 4 3 7 5
5 2 3 3 3 3 7 6
dim(X)=c(8,12)
X=t(X)
kmo(X)
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