kmo.r

# 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)