IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v82y2017i1d10.1007_s11336-016-9512-2.html
   My bibliography  Save this article

Asymptotic Robustness Study of the Polychoric Correlation Estimation

Author

Listed:
  • Shaobo Jin

    (Uppsala University)

  • Fan Yang-Wallentin

    (Uppsala University)

Abstract

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study. The numerical results show that the underlying normal distribution can be substantially biased, even though skewness and kurtosis are not large. The skew-normal assumption generally produces a lower bias than the normal assumption. Thus, it is worth using a non-normal distributional assumption if the normal assumption is dubious.

Suggested Citation

  • Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9512-2
    DOI: 10.1007/s11336-016-9512-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-016-9512-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-016-9512-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Albert Maydeu-Olivares, 2006. "Limited information estimation and testing of discretized multivariate normal structural models," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 57-77, March.
    2. Scharoun-Lee, Melissa & Adair, Linda S. & Kaufman, Jay S. & Gordon-Larsen, Penny, 2009. "Obesity, race/ethnicity and the multiple dimensions of socioeconomic status during the transition to adulthood: A factor analysis approach," Social Science & Medicine, Elsevier, vol. 68(4), pages 708-716, February.
    3. Berkane, Maia & Kano, Yutaka & Bentler, Peter M., 1994. "Pseudo maximum likelihood estimation in elliptical theory: Effects of misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 18(2), pages 255-267, September.
    4. Jose R.S. Santos & Caio L.N. Azevedo & Heleno Bolfarine, 2013. "A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(10), pages 2129-2149, October.
    5. Azevedo, Caio L.N. & Bolfarine, Heleno & Andrade, Dalton F., 2011. "Bayesian inference for a skew-normal IRT model under the centred parameterization," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 353-365, January.
    6. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    7. Anders Christoffersson & Anna Gunsjö, 1996. "A short note on the estimation of the asymptotic covariance matrix for polychoric correlations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 173-175, March.
    8. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    9. Ulf Olsson, 1979. "Maximum likelihood estimation of the polychoric correlation coefficient," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 443-460, December.
    10. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
    11. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    12. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    13. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    14. Fabrizio Durante, 2014. "The Skew-Normal and Related Families by Adelchi Azzalini," International Statistical Review, International Statistical Institute, vol. 82(3), pages 483-483, December.
    15. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    16. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    17. Carol Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    18. Carol M. Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    19. Heleno Bolfarine & Jorge Luis Bazan, 2010. "Bayesian Estimation of the Logistic Positive Exponent IRT Model," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 693-713, December.
    20. Dylan Molenaar & Conor Dolan & Paul Boeck, 2012. "The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 455-478, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandro Barbiero & Asmerilda Hitaj, 2020. "Goodman and Kruskal’s Gamma Coefficient for Ordinalized Bivariate Normal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 905-925, December.
    2. Shaobo Jin, 2022. "Frequentist Model Averaging in Structure Equation Model With Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1130-1145, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 581-612, December.
    2. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    3. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    4. Harry Joe & Alberto Maydeu-Olivares, 2010. "A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 393-419, September.
    5. Ke-Hai Yuan & Ying Cheng & Jeff Patton, 2014. "Information Matrices and Standard Errors for MLEs of Item Parameters in IRT," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 232-254, April.
    6. Steffen Grønneberg & Njål Foldnes, 2019. "A Problem with Discretizing Vale–Maurelli in Simulation Studies," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 554-561, June.
    7. Njål Foldnes & Steffen Grønneberg, 2019. "On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1000-1017, December.
    8. Steven P. Reise & Han Du & Emily F. Wong & Anne S. Hubbard & Mark G. Haviland, 2021. "Matching IRT Models to Patient-Reported Outcomes Constructs: The Graded Response and Log-Logistic Models for Scaling Depression," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 800-824, September.
    9. Sally Paganin & Christopher J. Paciorek & Claudia Wehrhahn & Abel Rodríguez & Sophia Rabe-Hesketh & Perry de Valpine, 2023. "Computational Strategies and Estimation Performance With Bayesian Semiparametric Item Response Theory Models," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 147-188, April.
    10. Scott Monroe, 2021. "Testing Latent Variable Distribution Fit in IRT Using Posterior Residuals," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 374-398, June.
    11. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4243-4258.
    12. Max Auerswald & Morten Moshagen, 2015. "Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 920-937, December.
    13. Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.
    14. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    15. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    16. Batiz-Zuk, Enrique & Christodoulakis, George & Poon, Ser-Huang, 2015. "Credit contagion in the presence of non-normal shocks," International Review of Financial Analysis, Elsevier, vol. 37(C), pages 129-139.
    17. Yang Liu, 2020. "A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 439-468, June.
    18. Douadia Bougherara & Laurent Piet, 2018. "On the role of probability weighting on WTP for crop insurance with and without yield skewness," Working Papers hal-02790605, HAL.
    19. Emanuela Raffinetti & Pier Alda Ferrari, 2021. "A dependence measure flow tree through Monte Carlo simulations," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(2), pages 467-496, April.
    20. Ick Hoon Jin & Minjeong Jeon, 2019. "A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 236-260, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:82:y:2017:i:1:d:10.1007_s11336-016-9512-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.