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Alain Giguère

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How many axes in your factor analysis? The little unknown history.

Categories: Food for thought

Posted on 12-13-10 at 11:47 a.m.

Image for How many axes in your factor analysis? The little unknown history.

Thoughts on the number of axes to be kept in a factor analysis, or how obsolete economic constraints still affect factor analysis.

Abstract

Market research  frequently uses factor analysis, especially in order to reduce the number of dimensions of the analysis space, get rid of residual noise, and set up the table for clustering or regression. A commonly used criterion to determine the number of axes to be kept is a minimum threshold (usually 1 or slightly above 1) to be applied to the associated eigenvalues – Kaiser Guttman rule (KG). This seems reasonable since a retained axis should carry at least as much information as every single variable on which the analysis space is built. What has always looked awkward to us, however, is that this criterion is applied before the axes rotation while the whole remaining analysis is performed after rotation. We will demonstrate through a few examples why it seems more logical to apply the criterion after rotation (in which case one does not talk about eigenvalues, but their equivalent: sum of squared loadings) and will tentatively suggest explanations of the current practice, one of which is rather unexpected. Finally, we shall shortly explain our own practice.

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