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Generalized Varying Coefficient Mediation Models

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Abstract

Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a two-layer generalized varying coefficient mediation model. This model captures the bridging effects of mediators that may vary with another variable, by treating them as smooth functions of this variable. It also allows various response types by introducing the generalized varying coefficient model in the first layer. The varying direct and indirect effects are estimated through spline expansion. The theoretical properties of the estimated direct and indirect coefficient functions including estimation biases, asymptotic distributions and so forth, are explored. Simulation studies validate the finite-sample performance of the proposed estimation method. A real data analysis based on the proposed model discovers some interesting behavioral economic phenomenon, that self-efficacy influences the deleterious impact of economic stress, both directly and indirectly through depressed affect, on business owners’ withdrawal intentions.

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References

  1. Bandura, A., Freeman, W., Lightsey, R.: Self-efficacy: The Exercise of Control (1997)

  2. Baron, R.A.: The role of affect in the entrepreneurial process. Acad. Manag. Rev. 33(2), 328–340 (2008)

    Article  Google Scholar 

  3. Baron, R.M., Kenny, D.A.: The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. J. Pers. Soc. Psychol. 51(6), 1173 (1986)

    Article  CAS  PubMed  Google Scholar 

  4. Baum, A., Fleming, R., Reddy, D.M.: Unemployment stress: loss of control, reactance and learned helplessness. Soc. Sci. Med. 22(5), 509–516 (1986)

    Article  CAS  PubMed  Google Scholar 

  5. Cai, Z., Fan, J., Li, R.: Efficient estimation and inferences for varying-coefficient models. J. Am. Stat. Assoc. 95(451), 888–902 (2000)

    Article  MathSciNet  Google Scholar 

  6. Chen, C.C., Greene, P.G., Crick, A.: Does entrepreneurial self-efficacy distinguish entrepreneurs from managers? J. Bus. Ventur. 13(4), 295–316 (1998)

    Article  Google Scholar 

  7. De Boor, C.: A Practical Guide to Splines. Springer, New York (1978)

    Book  Google Scholar 

  8. Dekker, S.W., Schaufeli, W.B.: The effects of job insecurity on psychological health and withdrawal: a longitudinal study. Aust. Psychol. 30(1), 57–63 (1995)

    Article  Google Scholar 

  9. Ditlevsen, S., Christensen, U., Lynch, J., et al.: A comparison of methods to test mediation and other intervening variable effects. Epidemiology 16, 114–120 (2005)

    Article  PubMed  Google Scholar 

  10. Egan, V., Tosanguan, P.: Coping strategies of entrepreneurs in economic recession: a comparative analysis of Thais and European expatriates in pattaya, thailand. J. Asia Entrepreneurship Sustain. 5(3), 17 (2009)

    Google Scholar 

  11. Hellgren, J., Sverke, M.: Does job insecurity lead to impaired well-being or vice versa? estimation of cross-lagged effects using latent variable modelling. J. Org. Behav.: Int. J. Ind. Occup. Org. Psychol. Behav. 24(2), 215–236 (2003)

    Article  Google Scholar 

  12. Huang, J.Z., Wu, C.O., Zhou, L.: Varying-coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89(1), 111–128 (2002)

    Article  MathSciNet  Google Scholar 

  13. Huang, J.Z., Wu, C.O., Zhou, L.: Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Stat. Sin. 14, 763–788 (2004)

    MathSciNet  Google Scholar 

  14. Huang, Y., Pan, W.: Hypothesis test of mediation effect in causal mediation model with high-dimensional continuous mediators. Biometrics 72(2), 402–413 (2016)

    Article  MathSciNet  PubMed  Google Scholar 

  15. Huang, Y., Vander Weele, T.X.L.: Joint analysis of SNP and gene expression data in genetic association studies of complex diseases. Ann. Appl. Stat. 8(1), 352 (2014)

    Article  MathSciNet  PubMed  PubMed Central  Google Scholar 

  16. Lange, T., Hansen, J.: Direct and indirect effects in a survival context. Epidemiology 22(4), 575–581 (2011)

    Article  PubMed  Google Scholar 

  17. Latham, S.: Contrasting strategic response to economic recession in start-up versus established software firms. J. Small Bus. Manag. 47(2), 180–201 (2009)

    Article  Google Scholar 

  18. Liao, Y., Liu, J., Coffman, D., et al.: Varying coefficient mediation model and application to analysis of behavioral economics data. J. Bus. Econ. Stat. https://doi.org/10.1080/07350015.2021.197108 (2021)

  19. Luo, C., Fa, B., Yan, Y., et al.: High-dimensional mediation analysis in survival models. PLoS Comput. Biol. 16(4), e1007,768 (2020)

    Article  Google Scholar 

  20. MacKinnon, D.P.: Introduction to Statistical Mediation Analysis. Routledge, New York (2008)

    Google Scholar 

  21. MacKinnon, D.P., Lockwood, C.M., Hoffman, J.M., et al.: A comparison of methods to test mediation and other intervening variable effects. Psychol. Methods 7(1), 83–104 (2002)

    Article  PubMed  PubMed Central  Google Scholar 

  22. Pollack, J.M., Vanepps, E.M., Hayes, A.F.: The moderating role of social ties on entrepreneurs’ depressed affect and withdrawal intentions in response to economic stress. J. Org. Behav. 33(6), 789–810 (2012)

    Article  Google Scholar 

  23. Seligman, M.E.: Learned helplessness. Annu. Rev. Med. 23(1), 407–412 (1972)

    Article  CAS  PubMed  Google Scholar 

  24. Sequeira, J., Mueller, S.L., McGee, J.E.: The influence of social ties and self-efficacy in forming entrepreneurial intentions and motivating nascent behavior. J. Dev. Entrep. 12(3), 275–293 (2007)

    Google Scholar 

  25. Sohn, M.B., Hongzhe, L.: Compositional mediation analysis for microbiome studies. Ann. Appl. Stat. 13(1), 661–681 (2019)

    Article  MathSciNet  Google Scholar 

  26. Valeri, L., Lin, X., VanderWeele, T.: Mediation analysis when a continuous mediator is measured with error and the outcome follows a generalized linear model. Stat. Med. 33(28), 4875–4890 (2014)

    Article  MathSciNet  PubMed  PubMed Central  Google Scholar 

  27. VanderWeele, T., Tchetgen, E.J.: Mediation analysis with time varying exposures and mediators. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 79(3), 917–938 (2017)

    Article  MathSciNet  Google Scholar 

  28. VanderWeele, T., Vansteelandt, S.: Odds ratios for mediation analysis for a dichotomous outcome. Am. J. Epidemiol. 172(12), 1339–1348 (2010)

    Article  PubMed  PubMed Central  Google Scholar 

  29. VanderWeele, T., Vansteelandt, S.: Mediation analysis with multiple mediators. Epidemiol. Methods 2(1), 95–115 (2014)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Verhasselt, A.: Generalized varying coefficient models. Stat. Sin. 24(1), 147–171 (2014)

    MathSciNet  Google Scholar 

  31. Wang, L., Zhang, Z.: Estimating and testing mediation effects with censored data. Struct. Equ. Model. 18(1), 18–34 (2011)

    Article  MathSciNet  CAS  Google Scholar 

  32. Wright, S.: On the nature of size factors. Genetics 3(4), 367 (1918)

    Article  MathSciNet  CAS  PubMed  PubMed Central  Google Scholar 

  33. Wright, S.: The method of path coefficients. Ann. Math. Stat. 5(3), 161–215 (1934)

    Article  Google Scholar 

  34. Yang, G., Yang, S., Li, R.: Feature screening in ultrahigh dimensional generalized varying-coefficient models. Stat. Sin. 30, 1049–1067 (2020)

    MathSciNet  PubMed  PubMed Central  Google Scholar 

  35. Zhou, R., Wang, L., Zhao, S.: Estimation and inference for the indirect effect in high-dimensional linear mediation models. Biometrika 107(3), 573–589 (2020)

    Article  MathSciNet  PubMed  Google Scholar 

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Acknowledgements

Liu’s research was supported by NNSFC 12271456, 71988101 and the Ministry of Education Research in the Humanities and Social Sciences 22YJA910002.

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Authors and Affiliations

  1. MOE Key Laboratory of Econometrics, Department of Statistics and Data Science, School of Economics, Wang Yanan Institute for Studies in Economics, Fujian Key Lab of Statistics, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Jingyuan Liu

  2. Department of Statistics, The Pennsylvania State University, University Park, PA, 16802, USA

    Yujie Liao & Runze Li

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  1. Jingyuan Liu
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  2. Yujie Liao
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  3. Runze Li
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Correspondence to Jingyuan Liu.

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Liu, J., Liao, Y. & Li, R. Generalized Varying Coefficient Mediation Models. Commun. Math. Stat. (2024). https://doi.org/10.1007/s40304-023-00366-2

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  • DOI: https://doi.org/10.1007/s40304-023-00366-2

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