Hello Roxane,

There is no one answer to which everyone will agree on this point.

The reason for the apparent popularity of salience thresholds of approximately .3 (as in your T & F citation) is that, if you square it, you get approximately 10% shared variation. Somebody decided that was a suitable guideline long ago. Now, on to different perspectives!

L. L. Thurstone's conceptual model of an ideal factor structure, which he called "simple structure," has each variable loading perfectly (e.g., correlation of +/- 1.0) on one and only one factor, and not at all (e.g., correlation of 0.0) on all other factors. Of course, real data sets would virtually never correspond to that requirement.

Raymond Cattell (a big contributor to the factor analysis literature) showed an example wherein a variable-factor loading of .15 was considered salient.

Richard Gorsuch (and others) discussed using statistical significance (e.g., is the variable-factor loading significantly different from zero) as a threshold, but dismissed it as being too sensitive to sample size.

Henry Kaiser (whose doctoral dissertation was development of the Varimax rotation scheme) suggested that a variable-factor loading was salient if it exceeded the root mean square value of all loadings on a given factor. I don't think I've ever seen this applied in a published study, however.

Everything else you find, for example, ad hoc guidelines of |.40| or better, or |.50| or better, which you appear to favor, or |.70| or better, are just that, ad hoc guidelines.

What is true is, the higher you set your threshold: (a) the fewer problems you'll have with cross-loadings (variables meeting the salience criterion on multiple factors); (b) the fewer variables you'll retain in your model, and likely fewer factors if you insist that a factor have at least 3 salient indicator variables; and (c) internal consistency reliability measures for the chosen variables (such as Cronbach's alpha) will tend to be higher.

As well, what is a reasonable criterion hinges on the nature of the variables in question, their expected relationships (e.g., from theory and/or prior study), and the factor extraction method used. For example, principal components analysis extraction generally biases loading estimates upwards in magnitude from what common factor analysis methods (e.g., principal axis, maximum likelihood) would yield, unless you have a lot of variables.

That said, you wanted a reference for ".50." Here's a link to a review paper in a completely different field (chosen on purpose) wherein the authors appear to be using a popularity contest approach to their recommendation of |.50| as a salience criterion: Article Use of exploratory factor analysis in maritime research

However, a thoughtful choice will always beat out an arbitrary one.

Good luck with your work!

Thank you so much for your complete answer :-)

Dear Roxane,

A higher minimum threshold would be appropriate with a smaller sample size. Have a look at the highly cited article by Guadagnoli and Velicet.