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Path Analysis for Binary Random Variables

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  • Martina Raggi
  • Elena Stanghellini
  • Marco Doretti

Abstract

The decomposition of the overall effect of a treatment into direct and indirect effects is here investigated with reference to a recursive system of binary random variables. We show how, for the single mediator context, the marginal effect measured on the log odds scale can be written as the sum of the indirect and direct effects plus a residual term that vanishes under some specific conditions. We then extend our definitions to situations involving multiple mediators and address research questions concerning the decomposition of the total effect when some mediators on the pathway from the treatment to the outcome are marginalized over. Connections to the counterfactual definitions of the effects are also made. Data coming from an encouragement design on students’ attitude to visit museums in Florence, Italy, are reanalyzed. The estimates of the defined quantities are reported together with their standard errors to compute p values and form confidence intervals.

Suggested Citation

  • Martina Raggi & Elena Stanghellini & Marco Doretti, 2023. "Path Analysis for Binary Random Variables," Sociological Methods & Research, , vol. 52(4), pages 1883-1915, November.
    • Handle: RePEc:sae:somere:v:52:y:2023:i:4:p:1883-1915
    DOI: 10.1177/00491241211031260
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    References listed on IDEAS

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    1. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    2. Patrizia Lattarulo & Marco Mariani & Laura Razzolini, 2017. "Nudging museums attendance: a field experiment with high school teens," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 41(3), pages 259-277, August.
    3. Patrizia Lattarulo & Marco Mariani & Laura Razzolini, 2017. "Erratum to: Nudging museums attendance: a field experiment with high school teens," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 41(3), pages 279-281, August.
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