Title: A Generalized Polychoric Correlation Coefficient Assuming an Underlying
Bivariate Mixture Distribution

Authors: Laura Kolbe, Frans J. Oort, Suzanne Jak

Affiliation: University of Amsterdam

Abstract:
The polychoric correlation coefficient is a measure of association between two
ordinal variables. One assumption of this coefficient is underlying bivariate
normality. That is, the observed responses to the ordinal variables are
assumed to be generated by two underlying continuous variables that follow a
bivariate normal distribution. This assumption can be tested for a given pair
of ordinal variables with the likelihood ratio test. When the underlying
bivariate normality assumption is violated, the estimated polychoric
correlation coefficient may be biased. In this talk, I will illustrate
existing generalizations of the polychoric correlation coefficient in which
the assumption of underlying bivariate normality is relaxed to underlying
bivariate skewed normality and underlying bivariate normal mixtures.