Swamy, A. Burmawala

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This function computes the Kaiser-Meyer-Olkin (KMO) criterion overall and for each variable in a correlation matrix. The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis.

Kaiser (1970) proposed this index, originally called measure of sampling adequacy (MSA), that indicates how near the inverted correlation matrix R^{-1} is to a diagonal matrix S to determine a given correlation matrix's (R) suitability for factor analysis. The index is

KMO = \frac{\sum\limits_{i

with Q = SR^{-1}S and S = (diag R^{-1})^{-1/2} where \sum\limits_{i

So KMO varies between 0 and 1, with larger values indicating higher suitability for factor analysis. Kaiser and Rice (1974) suggest that KMO should at least exceed .50 for a correlation matrix to be suitable for factor analysis.

This function was heavily influenced by the psych::KMO function.

See also BARTLETT for another test of suitability for factor analysis.

The KMO function can also be called together with the BARTLETT function and with factor retention criteria in the N_FACTORS function.

A list containing

Kaiser, H. F. (1970). A second generation little jiffy. Psychometrika, 35, 401-415.

Kaiser, H. F. & Rice, J. (1974). Little jiffy, mark IV. Educational and Psychological Measurement, 34, 111-117.

Cureton, E. E. & D'Augustino, R. B. (1983). Factor analysis: An applied approach. Hillsdale, N.J.: Lawrence Erlbaum Associates, Inc.

BARTLETT for another measure to determine suitability for factor analysis.

N_FACTORS as a wrapper function for this function, BARTLETT and several factor retention criteria.

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