IDEAS home Printed from
   My bibliography  Save this article

Intra-class correlation in random-effects models for binary data


  • German Rodriguez

    (Princeton University)

  • Irma Elo

    (The University of Pennsylvania)


We review the concept of intra-class correlation in random-effects models for binary outcomes as estimated by Stata's xtprobit, xtlogit, and xtclog. We consider the usual measures of correlation based on a latent variable formulation of these models and note corrections to the last two procedures. We also discuss alternative measures of association based on manifest variables or actual outcomes and introduce a new command xtrho for computing these measures for all three types of models. Copyright 2003 by Stata Corporation.

Suggested Citation

  • German Rodriguez & Irma Elo, 2003. "Intra-class correlation in random-effects models for binary data," Stata Journal, StataCorp LP, vol. 3(1), pages 32-46, March.
  • Handle: RePEc:tsj:stataj:v:3:y:2003:i:1:p:32-46

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    6. Martin S. Eichenbaum & Lars Peter Hansen & Kenneth J. Singleton, 1988. "A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 103(1), pages 51-78.
    7. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
    8. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    9. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
    10. Cumby, Robert E. & Huizinga, John & Obstfeld, Maurice, 1983. "Two-step two-stage least squares estimation in models with rational expectations," Journal of Econometrics, Elsevier, vol. 21(3), pages 333-355, April.
    11. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-763, May.
    12. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    13. Caroline Hoxby & M. Daniele Paserman, 1998. "Overidentification Tests with Grouped Data," NBER Technical Working Papers 0223, National Bureau of Economic Research, Inc.
    14. Pesaran, M Hashem & Taylor, Larry W, 1999. " Diagnostics for IV Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 255-281, May.
    15. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    16. Nakamura, Alice & Nakamura, Masao, 1981. "On the Relationships among Several Specification Error Tests Presented by Durbin, Wu, and Hausman," Econometrica, Econometric Society, vol. 49(6), pages 1583-1588, November.
    17. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    18. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
    19. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    20. John Shea, 1997. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 348-352, May.
    21. Godfrey, Leslie G., 1978. "Testing for multiplicative heteroskedasticity," Journal of Econometrics, Elsevier, vol. 8(2), pages 227-236, October.
    22. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Sun-Joo Cho & Jennifer Gilbert & Amanda Goodwin, 2013. "Explanatory Multidimensional Multilevel Random Item Response Model: An Application to Simultaneous Investigation of Word and Person Contributions to Multidimensional Lexical Representations," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 830-855, October.
    2. Luis Sagaon TEYSSIER & Nawal ZAAJ, 2015. "Hazard analysis for interval-censored duration of non-employment: school-to-work transition of vocational training graduates in Morocco," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 15(2), pages 161-178.
    3. Martin Srholec, 2015. "Understanding the diversity of cooperation on innovation across countries: multilevel evidence from Europe," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 24(1-2), pages 159-182, March.
    4. Erik R. Vickstrom, 2014. "Legal Status, Territorial Confinement, and Transnational Activities of Senegalese Migrants in France, Italy, and Spain," Working Papers 15-01h, Princeton University, Woodrow Wilson School of Public and International Affairs, Center for Migration and Development..
    5. Dr Alex Bryson, 2011. "Change and Persistence in the German Model of Collective Bargaining and Worker Representation," National Institute of Economic and Social Research (NIESR) Discussion Papers 382, National Institute of Economic and Social Research.
    6. Judith Offerhaus, 2013. "The Type to Train?: Impacts of Personality Characteristics on Further Training Participation," SOEPpapers on Multidisciplinary Panel Data Research 531, DIW Berlin, The German Socio-Economic Panel (SOEP).
    7. Addison, John T. & Teixeira, Paulino & Bryson, Alex & Pahnke, André, 2011. "The Structure of Collective Bargaining and Worker Representation: Change and Persistence in the German Model," IZA Discussion Papers 5987, Institute for the Study of Labor (IZA).
    8. Soto, José R. & Adams, Damian C. & Escobedo, Francisco J., 2016. "Landowner attitudes and willingness to accept compensation from forest carbon offsets: Application of best–worst choice modeling in Florida USA," Forest Policy and Economics, Elsevier, vol. 63(C), pages 35-42.
    9. Khudnitskaya, Alesia S., 2009. "Microenvironment-specific Effects in the Application Credit Scoring Model," MPRA Paper 23175, University Library of Munich, Germany.
    10. Damien Rousselière & Iragaël Joly, 2011. "A propos de la capacité à survivre des coopératives : une étude de la relation entre âge et mortalité des organisations coopératives agricoles françaises," Review of Agricultural and Environmental Studies - Revue d'Etudes en Agriculture et Environnement, INRA Department of Economics, vol. 92(3), pages 259-289.
    11. John T. Addison & Paulino Teixeira & Alex Bryson & André Pahnke, 2013. "Collective Agreement Status and Survivability: Change and Persistence in the German Model," LABOUR, CEIS, vol. 27(3), pages 288-309, September.
    12. Lan Vu & Linh Le & Nazeem Muhajarine, 2013. "Multilevel Determinants of Colleges/Universities Enrolment in Vietnam: Evidences from the 15% Sample Data of Population Census 2009," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 111(1), pages 375-386, March.
    13. Addison, John T. & Teixeira, Paulino & Evers, Katalin & Bellmann, Lutz, 2013. "Collective Bargaining and Innovation in Germany: Cooperative Industrial Relations?," IZA Discussion Papers 7871, Institute for the Study of Labor (IZA).
    14. Jeffrey T. Macher & John W. Mayo, 2015. "Influencing public policymaking: Firm-, industry-, and country-level determinants," Strategic Management Journal, Wiley Blackwell, vol. 36(13), pages 2021-2038, December.
    15. Nauleau, Marie-Laure, 2014. "Free-riding on tax credits for home insulation in France: An econometric assessment using panel data," Energy Economics, Elsevier, vol. 46(C), pages 78-92.
    16. Yue, Chen & Chen, Shaojie & Sair, Haris I. & Airan, Raag & Caffo, Brian S., 2015. "Estimating a graphical intra-class correlation coefficient (GICC) using multivariate probit-linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 126-133.
    17. Conroy, Amy A. & Wong, Lauren H., 2015. "How reliable are self-reports of HIV status disclosure? Evidence from couples in Malawi," Social Science & Medicine, Elsevier, vol. 144(C), pages 28-37.
    18. Boyd Hunter & Matthew Gray & Ben Edwards, 2013. "The Use of Social Surveys to Measure Drought and the Impact of Drought," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 113(1), pages 419-432, August.


    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:tsj:stataj:v:3:y:2003:i:1:p:32-46. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum) or (Lisa Gilmore). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.