1. A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization
- Author
-
Sema Atis, Fatma Ezgi Can, Ilker Ercan, Hakan Demirtas, Robab Ahmadian, Uludağ Üniversitesi/Tıp Fakültesi/Biyoistatistik Anabilim Bölümü., Ahmadian, Robab, Atış, Sema, Can, Fatma Ezgi, Ercan, İlker, and AAE-5602-2019
- Subjects
Statistics and Probability ,Coefficient ,Discretization ,Random number generation ,Performance ,Generation ,Threshold concept ,Bivariate analysis ,01 natural sciences ,Continuous variable ,Correlation ,010104 statistics & probability ,0504 sociology ,Statistics ,Pattern-mixture models ,Applied mathematics ,Ordinal data ,0101 mathematics ,Ignorable drop-out ,Mathematics ,Nonnormality ,05 social sciences ,Spectrum (functional analysis) ,050401 social sciences methods ,Polychoric correlation ,Marginal Distribution ,Simulation ,Normalizing Transformation ,Connection (mathematics) ,Computational Mathematics ,Multiple imputation ,Power polynomials ,Distributions ,Statistics, Probability and Uncertainty ,Statistics & probability - 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.
- Published
- 2016
- Full Text
- View/download PDF