Kaiser-Meyer-Olkin measure for identity correlation matrix

Troubleshooting

Problem

I have run a factor analysis in IBM SPSS Statistics with the FACTOR command (Analyze>Dimension Reduction>Factor). I requested measures of sampling adequacy by checking the boxes for "KMO and Bartlett's test of sphericity" and "Anti-image" in the Descriptives dialog of the Factor procedure. (They are also available by adding the keywords KMO and AIC, respectively, in the /PRINT subcommand of the FACTOR command. ) Given the formula for the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy in the Factor chapter in the SPSS Statistical Algorithms manual, it seems that KMO should be undefined when the correlation matrix is an identity matrix. All of the off-diagonal correlations and partial correlations should be 0 in this situation, so the KMO should be 0/(0+0) and therefore undefined. However, KMO is printed as .5 when the correlation matrix is an identity matrix. Is .5 inserted arbitrarily when KMO is undefined?

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Historical Number

37366

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Document Information

Modified date:
16 April 2020

UID

swg21479963

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