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Correlations and Nonlinear Probability Models


  • Richard Breen

    (Center for Research on Inequality and the Life Course, Department of Sociology, Yale University, New Haven, CT, USA)

  • Anders Holm

    (Department of Sociology, University of Copenhagen, Copenhagen, Denmark
    SFI—The Danish National Centre for Social Research, Copenhagen, Denmark)

  • Kristian Bernt Karlson

    (Department of Sociology, University of Copenhagen, Copenhagen, Denmark)


Although the parameters of logit and probit and other nonlinear probability models (NLPMs) are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of NLPMs, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of NLPMs.

Suggested Citation

  • Richard Breen & Anders Holm & Kristian Bernt Karlson, 2014. "Correlations and Nonlinear Probability Models," Sociological Methods & Research, , vol. 43(4), pages 571-605, November.
  • Handle: RePEc:sae:somere:v:43:y:2014:i:4:p:571-605

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    Cited by:

    1. Gerhard Tutz, 2020. "Modelling heterogeneity: on the problem of group comparisons with logistic regression and the potential of the heterogeneous choice model," 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(3), pages 517-542, September.
    2. Peter Fallesen & Richard Breen, 2016. "Temporary Life Changes and the Timing of Divorce," Demography, Springer;Population Association of America (PAA), vol. 53(5), pages 1377-1398, October.
    3. Pakpahan, Eduwin & Hoffmann, Rasmus & Kröger, Hannes, 2017. "The long arm of childhood circumstances on health in old age: Evidence from SHARELIFE," EconStor Open Access Articles, ZBW - Leibniz Information Centre for Economics, pages 1-10.
    4. Swain, Swadhina Shikha & Mishra, Pulak, 2021. "How does cleaner energy transition influence standard of living and natural resources conservation? A study of households’ perceptions in rural Odisha, India," Energy, Elsevier, vol. 215(PB).
    5. Jouni Kuha & Colin Mills, 2020. "On Group Comparisons With Logistic Regression Models," Sociological Methods & Research, , vol. 49(2), pages 498-525, May.
    6. Anders Holm & Mette Ejrnæs & Kristian Karlson, 2015. "Comparing linear probability model coefficients across groups," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 1823-1834, September.
    7. Kuha, Jouni & Mills, Colin, 2017. "On Group Comparisons with Logistic Regression Models," SocArXiv gwck3, Center for Open Science.
    8. Kuha, Jouni & Mills, Colin, 2018. "On group comparisons with logistic regression models," LSE Research Online Documents on Economics 84163, London School of Economics and Political Science, LSE Library.


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