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

Hakan Demirtas (), Robab Ahmadian, Sema Atis, Fatma Ezgi Can and Ilker Ercan
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Hakan Demirtas: University of Illinois at Chicago
Robab Ahmadian: Uludag University
Sema Atis: Uludag University
Fatma Ezgi Can: Uludag University
Ilker Ercan: Uludag University

Computational Statistics, 2016, vol. 31, issue 4, No 8, 1385-1401

Abstract: 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.

Keywords: Random number generation; Simulation; Nonnormality; Threshold concept (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00180-016-0653-7

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