IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v70y2016i2p143-148.html
   My bibliography  Save this article

A Note on the Relationship Between the Phi Coefficient and the Tetrachoric Correlation Under Nonnormal Underlying Distributions

Author

Listed:
  • Hakan Demirtas

Abstract

The connection between the phi coefficient and the tetrachoric correlation is well-understood when the underlying distribution is bivariate normal. For many other bivariate distributions, the identity that links these two quantities together is not straightforward to formulate. Furthermore, even when this can be done, solving the equation in either direction may be far from trivial. We propose a simple technique that enables students and researchers to compute one of these correlations when the other is specified. Generalizing the normal-based results to a broad range of bivariate distributional setups is potentially useful in graduate-level teaching as well as in simulation studies that involve dichotomization and random number generation where the relationships between these correlation types need to be modeled.

Suggested Citation

  • Hakan Demirtas, 2016. "A Note on the Relationship Between the Phi Coefficient and the Tetrachoric Correlation Under Nonnormal Underlying Distributions," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 143-148, May.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:2:p:143-148
    DOI: 10.1080/00031305.2015.1077161
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2015.1077161
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2015.1077161?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. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. repec:jss:jstsof:19:i03 is not listed on IDEAS
    5. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    6. Oscar L. Olvera Astivia & Bruno D. Zumbo, 2019. "A Note on the Solution Multiplicity of the Vale–Maurelli Intermediate Correlation Equation," Journal of Educational and Behavioral Statistics, , vol. 44(2), pages 127-143, April.
    7. Headrick, Todd C. & Sheng, Yanyan & Hodis, Flaviu-Adrian, 2007. "Numerical Computing and Graphics for the Power Method Transformation Using Mathematica," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i03).
    8. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    9. Mahul, Olivier, 2002. "Hedging Price Risk in the Presence of Crop Yield and Revenue Insurance," 2002 International Congress, August 28-31, 2002, Zaragoza, Spain 24881, European Association of Agricultural Economists.
    10. 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.
    11. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    12. 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.
    13. Al-Subaihi, Ali A., 2004. "Simulating Correlated Multivariate Pseudorandom Numbers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i04).
    14. Rainer Schlittgen & Marko Sarstedt & Christian M. Ringle, 2020. "Data generation for composite-based structural equation modeling methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(4), pages 747-757, December.
    15. Theo Dijkstra & Karin Schermelleh-Engel, 2014. "Consistent Partial Least Squares for Nonlinear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 585-604, October.
    16. Pasquale Dolce & Cristina Davino & Domenico Vistocco, 2022. "Quantile composite-based path modeling: algorithms, properties and applications," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 909-949, December.
    17. Headrick, Todd C. & Mugdadi, Abdel, 2006. "On simulating multivariate non-normal distributions from the generalized lambda distribution," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3343-3353, July.
    18. Gary van Vuuren & Riaan de Jongh, 2017. "A comparison of risk aggregation estimates using copulas and Fleishman distributions," Applied Economics, Taylor & Francis Journals, vol. 49(17), pages 1715-1731, April.
    19. Ke-Hai Yuan & Peter Bentler, 2002. "On robusiness of the normal-theory based asymptotic distributions of three reliability coefficient estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 251-259, June.
    20. repec:jss:jstsof:09:i04 is not listed on IDEAS
    21. Kiero Guerra-Peña & Zoilo Emilio García-Batista & Sarah Depaoli & Luis Eduardo Garrido, 2020. "Class enumeration false positive in skew-t family of continuous growth mixture models," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-19, April.
    22. Paul Dudgeon, 2017. "Some Improvements in Confidence Intervals for Standardized Regression Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 928-951, December.

    More about this item

    Statistics

    Access and download statistics

    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:taf:amstat:v:70:y:2016:i:2:p:143-148. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UTAS20 .

    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.