A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization


Demirtas H., Ahmadian R., Atis S., Can F. E. , ERCAN İ.

COMPUTATIONAL STATISTICS, vol.31, no.4, pp.1385-1401, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1007/s00180-016-0653-7
  • Title of Journal : COMPUTATIONAL STATISTICS
  • Page Numbers: pp.1385-1401

Abstract

Two algorithms for establishing a connection between correlations before and after ordinalization under a wide spectrum of nonnormal underlying bivariate distributions are developed by extending the iteratively found normal-based results via the power polynomials. These algorithms are designed to compute the polychoric correlation when the ordinal correlation is specified, and vice versa, along with the distributional properties of latent, continuous variables that are subsequently ordinalized through thresholds dictated by the marginal proportions. The method has broad applicability in the simulation and random number generation world where modeling the relationships between these correlation types is of interest.