Making sense of numbers and words: Statistical methods

Peter Grimbeek

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Exploratory factor analysis

In conversation a while ago, I discussed the essentials of reporting for exploratory factor analysis. These include of course the KMO estimate of factorability (equivalent to Cronbach's alpha), Bartlett's test of symmetry (preferably significant), cumulative variance explained (if factors rotated orthogonally -e.g., Varimax), the type of factor extraction (principal components - not highly regarded but robust; principal axis factoring - takes error variance into account; maximum likelihood-default for structural equation modeling and handy if wish to align exploratory and confirmatory factor analyses).

Then there are the number of factors, the simplicity of the factor structure, and the intelligibility of item clusters.

One could also report the estimates of communalities (preferably 0.5 or better).

What doesn't always get a mention is the need to screen items prior to analysis with the aim of excluding highly skewed items (90% or better of responses falling in one response category). Another thing to consider is the collinearity of items.
While orthogonal rotation methods produce independent components, and this is preferable because the cumulative variance per component (factor) is additive, oblique or non-orthogonal (e.g., Oblimin) rotations make sense where responses across factors are likely to be correlated (i.e., the individual responding to these items does not treat them as expressing clearly distinct factors).