Correlation coefficients for ordered data: Kendall’s Tau vs Polychoric vs Spearman’s rho

It seems like for managing with ordered measurements researchers usually deal with Polychoric Correlation. (For example, for making matrix before doing Factor Analysis.) Why so?

Kendall Tau Rank Correlation Coefficient and Spearman’s rank correlation coefficient are also suitable for ordered data.

Any points ‘pro’ and ‘contra’ for these correlation coefficients are welcome.


Partially answered in comments:

As your Wikipedia link states, the polychoric correlation assumes that the manifest ordinal variables come from categorizing latent normal variables; Kendall’s tau & Spearman’s correlation do not assume this. Other than that, the differences are covered in Kendall Tau or Spearman’s rho? If there is anything left that isn’t already covered, please edit to clarify. – gung

( Does it mean that Polychoric is less suitable in general case? – drobnbobn )

It means polychoric is appropriate when the manifest ordinal variables came from categorizing latent normal variables & not otherwise. (In practice, it’s more like when you are willing to assume this & not otherwise, since you will rarely know & can’t really check the assumption.) OTOH, it probably doesn’t make much difference in most cases, for an analogy, see my answer here: Difference between logit and probit models. – gung

Source : Link , Question Author : drobnbobn , Answer Author : kjetil b halvorsen

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