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Correlations and Nonlinear Probability Models

Author

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  • Richard Breen
  • Anders Holm
  • Kristian Bernt Karlson

Abstract

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
    DOI: 10.1177/0049124114544224
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    Cited by:

    1. 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).
    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. Jouni Kuha & Colin Mills, 2020. "On Group Comparisons With Logistic Regression Models," Sociological Methods & Research, , vol. 49(2), pages 498-525, May.
    4. J. Scott Long & Sarah A. Mustillo, 2021. "Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes," Sociological Methods & Research, , vol. 50(3), pages 1284-1320, August.
    5. 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 and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 31, pages 1-10.
    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. 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.
    8. Kuha, Jouni & Mills, Colin, 2017. "On Group Comparisons with Logistic Regression Models," SocArXiv gwck3, Center for Open Science.
    9. 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.
    10. Janna Besamusca, 2020. "The short or long end of the stick? Mothers’ social position and self‐employment status from a comparative perspective," Gender, Work and Organization, Wiley Blackwell, vol. 27(6), pages 1285-1307, November.
    11. Schulz, Dario & Börner, Jan, 2021. "Context and Technology Traits Explain Heterogeneity Across Adoption Studies of Agricultural Innovations: A Global Meta-Analysis," 2021 Conference, August 17-31, 2021, Virtual 315003, International Association of Agricultural Economists.

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