|W Binary||X Categorical||Y Ordinal||Z Numerical|
- binary variables <-> tetrachoric correlation is a special case of the polychoric correlation
- categorical variables<->polychoric correlation
- Ordinal variables<-> polychoric correlations
- Numerical variables <->Pearson correlations
- numeric and ordinal data<->polyserial correlations
The polychoric correlation coefficient, ρ, is used for correlation when the data consist of observations from two ordinal variables, each having an arbitrary number of response categories.
The polychoric correlation coefficient estimates the correlation between two unobserved bivariate normal variables assumed to underlie the observed ordinal variables.
The polychoric correlation coefficient is a generalization of the tetrachoric correlation coefficient, a statistic used to estimate correlation based on two dichotomous variables.
Under assumptions, the polychoric correlation provides a correlation estimate that is entirely free of the attenuation caused when two normally distributed variables are “crudely categorized”-that is, when they are reduced to sets of ordinal categories.