# What is Polychoric Correlation Coefficient intuitively?

There is clear meaning of Pearson product-moment correlation coefficient:

it is cosine of angle between two vectors based on variables.

Also there are 12 other ways to clearify the meaning of Pearson correlation.

Is there any similar for Polychoric correlation coefficient? Besides just "correlation between two ordinal variables" and without complicated formulas.

• Check Chi's answer to this question for a start: Differences between tetrachoric and Pearson correlation and john-uebersax.com/stat/tetra.htm – user20650 Dec 6 '13 at 0:44
• @user20650 I already have studied this link before. It is a good paper, but not complete and mainly aimed at Tetrachoric. I think there should be some textbooks with better description. – drobnbobn Dec 6 '13 at 0:53
• The referenced answer is presumably @chl's here: Differences between tetrachoric and Pearson correlation. – gung Aug 16 '17 at 20:27
• Polychoric correlation is an inferred Pearson correlation. It is not correlation between ordinal variables, it is correlation between "underlying" continuous variables whereof the ordinal variables are seen as the result of binning. When there is only 2 levels in the ordinal variables, it is called tetrachoric correlation. – ttnphns Aug 16 '17 at 20:31

To quote the authors (from the help-file for their polychoric Stata command):