  While five-factor models of personality are widespread, there is still not
universal agreement on this as a structural framework. Part of the reason for
the lingering debate is its dependence on factor analysis. In particular,
derivation or refutation of the model via other statistical means is a
worthwhile project. In this paper we use the methodology of spectral clustering
to articulate the structure in the dataset of responses of 20,993 subjects on a
300-item item version of the IPIP NEO personality questionnaire, and we compare
our results to those obtained from a factor analytic solution. We found support
for five- and six-cluster solutions. The five-cluster solution was similar to a
conventional five-factor solution, but the six-cluster and six-factor solutions
differed significantly, and only the six-cluster solution was readily
interpretable: it gave a model similar to the HEXACO model. We suggest that
spectral clustering provides a robust alternative view of personality data.
