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

Author

Listed:
  • Hakan Demirtas

    (University of Illinois at Chicago)

  • Robab Ahmadian

    (Uludag University)

  • Sema Atis

    (Uludag University)

  • Fatma Ezgi Can

    (Uludag University)

  • Ilker Ercan

    (Uludag University)

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.

Suggested Citation

  • Hakan Demirtas & Robab Ahmadian & Sema Atis & Fatma Ezgi Can & Ilker Ercan, 2016. "A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization," Computational Statistics, Springer, vol. 31(4), pages 1385-1401, December.
  • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-016-0653-7
    DOI: 10.1007/s00180-016-0653-7
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    References listed on IDEAS

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    1. Demirtas, Hakan & Arguelles, Lester M. & Chung, Hwan & Hedeker, Donald, 2007. "On the performance of bias-reduction techniques for variance estimation in approximate Bayesian bootstrap imputation," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4064-4068, May.
    2. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    3. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    4. Amatya, Anup & Demirtas, Hakan, 2015. "OrdNor: An R Package for Concurrent Generation of Correlated Ordinal and Normal Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 68(c02).
    5. Hakan Demirtas, 2004. "Simulation driven inferences for multiply imputed longitudinal datasets," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 466-482, November.
    6. Demirtas, Hakan & Hedeker, Donald, 2011. "A Practical Way for Computing Approximate Lower and Upper Correlation Bounds," The American Statistician, American Statistical Association, vol. 65(2), pages 104-109.
    7. Headrick, Todd C., 2002. "Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 685-711, October.
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