I have a dataset of 77 items, ranked by 17 people, with many ties (actually: Q-sorted under a forced quasi-normal distribution in 15 bins). I am interested in common patterns of sorting items across people, so I want some exploratory factor analysis (PCA or PAF, probably) with items as cases, and people as variables (I know, it's odd - it's called Q Methodology.
The end result should be factor scores on these items, as "ideal-typical" ways to rank order these items. (Again, that's not me, that's Q).
I want to assume / preserve the ordinal nature of this data, so that leaves Spearman's or Kendall's as correlation coefficients for the correlation matrix. (I'm vaguely aware of Polychoric correlations, but I have no idea how that works, so I'd rather not touch it).
Two questions:
- Can I use PAF and/or PCA on a Spearman's and/or Kendall's correlation coefficient?
- How would I have to interpret the results differently (from a Pearson's based PAF/PCA) – if at all?
I know there are some answers around this issue, but there remains disagreement in answers and comments, as well as the literature. Also, the Q-circumstances are a bit special (or not, I don't know).
- This A seems to suggest Spearman works (no word on Kendall), though with different interpretation.
- This Q on SSCP seems to have to do with it.
- This A says "classic (linear) factor analysis" is only for Pearson's
- Basilevsky 2009 says "A Factor analysis can be based on a correlation matrix using Kendall's tau. Nothing new of major importance arises with respect to the interpretation of the results (...).
Ps.: since this (also) pertains to Q-Methodology, I'd appreciate if someone could add qmethod as a tag; see QMethod for a description and more.
