The Wikipedia page for the Kaiser–Meyer–Olkin test says that KMO "is a measure of the proportion of variance among variables that might be common variance."
So you will see people get an overall KMO of say .9, and then they say “This means that common factors might explain 90% of the variability in my observed variables”.
Other questions have discussed the KMO. I understand that a high KMO means that full correlations are large relative to partial correlations. From this question I understand that it makes sense that for factor analysis we should not want high partial correlations relative to full correlations, since high partial correlations implicate the existence of factors that load only two variables.
However, I don't see how that maps onto the idea that the overall KMO measures "the proportion of variance among variables that might be common variance" as per Wikipedia.
Why is it the proportion of variance among variables that might be common variance? What assumptions does this “might” depend on?
Obtaining the overall KMO value does not require specifying the number of factors to extract. However, is not the amount of variance explained by the factors determined by the number of factors that we extract, with all 100% of variance explained by factors if the number of factors equals the number of variables? I know that in practice computer programs will generally not allow there to be as many as factors.
