Witold, the polychoric correlation is a correlation of categorical variables. There are two assumptions, i.e., continuous latent variables underlying the contingency table, and a joint distribution of corresponding standard normal deviates that is bivariate normal.

HTH, Karin

Witold, the polychoric correlation is a correlation of categorical variables. There are two assumptions, i.e., continuous latent variables underlying the contingency table, and a joint distribution of corresponding standard normal deviates that is bivariate normal.

HTH, Karin

Hello Karin,

It makes perfect sense now as this type of correlation was applied in a paper using CFA on latent construct and WLSMV estimator was used for categorical variables which was recommended by Flora and Curran (2004). 

Thank you again

Hey Witold,

if you use the poylchoric correlation one has in mind that an ordinal categorical variable is the result of an categorized continuous random variable.

The polychoric correlation estimates the correlation between the underlying continuous random variables while the Bravais-Pearson correlation (product-moment correlation) estimates the correlation between the two categorical random variables.

The second assumption Karin mentioned can be relaxed. Kukuk (1998) showed that the PC correlation is only slightly biased as long as the latent variables are jointly symmetrically and elliptically distributed with a moderate kurtosis.

Kind regards,

Florian  

Kukuk, M. (1998). Analyszing ordered categorical data derived from elliptically symmetric distributions.