Path Analysis for Binary Random Variables

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...

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Bibliographic Details
Published in:Sociological methods & research 2023-11, Vol.52 (4), p.1883-1915
Main Authors: Raggi, Martina, Stanghellini, Elena, Doretti, Marco
Format: Article
Language:English
Subjects:
Error of Measurement
Foreign Countries
Graphs
Indirect effects
Marginality
Museums
Path Analysis
Random variables
Regression (Statistics)
Student Attitudes
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Summary: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.
ISSN:0049-1241
1552-8294
DOI:10.1177/00491241211031260