On the Kaiser-Meier-Olkin’s Measure of Sampling Adequacy

Abstract

The paper examines the suitability of the Kaiser-Meier Olkin’s Measure of Sampling Adequacy (KMO) as a measure of suitability for factor analysis for a number of selected multivariate datasets. It first explores a systematic approach that determines the initial dimensionality of the dataset. It then identifies two sets of indicators that could create distortions in assessing factor-suitability: variables that do not influence any dimension; and those that influence multiple dimensions. Dimensionality is also affected by negatively correlated indicators leading to a small suitability measure, which portrays such datasets as unsuitable for factor analysis. It is found that for KMO to be high, the zero- and first-order partial correlations must be almost the same for indicators that influence the same dimension. It follows that generally, a KMO value within the range 0.6 – 0.7 is a typically good measure of factor-suitability. The results show that the overall KMO generally reflects factor-suitability. The study does not find the expected intuitive relation that should exist between the individual KMO value and the communality for a suitably selected factor solution. A high variable KMO appears to be associated with moderate value of coefficient of multiple determination of its model in terms of the others. A reasonable assessment of the KMO should therefore be made only by a good understanding of the correlation structure of the indicator variables.

Keywords: KMO, Factor-suitability, Factor analysis, Dimensionality