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  • Mediation analysis with two mediators and binary outcome variable

    Hi everyone,
    I’m looking for advice on how to conduct mediation analysis in a situation where:
    • The treatment (X) is binary
    • There are two mediators (M1 and M2) which are continuous and correlated with one another (~0.65)
    • The outcome (Y) is binary
    • I have controls (C1–C3)
    • I want to incorporate survey weights due to complex survey design.
    I’ve tried paramed but it doesn’t seem to support simultaneous mediation with two correlated mediators. sureg doesn’t support a binary outcome.
    I then tried gsem with the following model specification:

    Code:
    gsem (M1 <- X C1 C2 C3, family(gaussian)) ///
         (M2 <- X C1 C2 C3, family(gaussian)) ///
         (Y <- X M1 M2 C1 C2 C3, family(binomial) link(logit)) [pweight=W], ///
         nocapslatent covariance(e.M1*e.M2)
    To estimate indirect effects, I used:

    Code:
     nlcom (indirect_M1: _b[M1:X]*_b[Y*M1]) ///
          (indirect_M2: _b[M2:X]*_b[Y*M2]) ///
          (total_indirect: (_b[M1:X]*_b[Y*M1]) + (_b[M2:X]*_b[Y*M2])) ///
          (total_effect: _b[Y*X] + (_b[M1:X]*_b[Y*M1]) + (_b[M2:X]*_b[Y*M2]))
    With this code, I get the following results:

    Code:
    -------------------------------------------------------------------------------
                  | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
    --------------+----------------------------------------------------------------
     indirect_M1 |   .0602089   .0125258     4.81   0.000     .0356588     .084759
     indirect_M2 |   .1230778    .017646     6.97   0.000     .0884922    .1576634
    total_indir~t |   .1832867   .0232965     7.87   0.000     .1376263     .228947
     total_effect |   .6485873   .0899088     7.21   0.000     .4723693    .8248052

    My questions:
    • I’m new to mediation analysis and want to confirm whether my approach is valid: Is it appropriate to model mediation with two correlated continuous mediators simultaneously in gsem when the outcome is binary? Being new to mediation analysis and gsem, I’d also be grateful for any help interpreting these results.
    • Am I correctly specifying the covariance of residuals between the two mediators using covariance(e.M1*e.M2) in the gsem command?
    • Is my nlcom syntax correct for estimating the indirect effects through each mediator, their total indirect effect, and the total effect?
    • Regarding survey weights: Am I incorporating them properly in this gsem mediation model? I notice that weighted and unweighted results (the latter are reported below) differ substantially. The dataset documentation recommends always using weights to account for complex survey design.
    Unweighted results:

    Code:
    -------------------------------------------------------------------------------
                  | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
    --------------+----------------------------------------------------------------
     indirect_M1 |    .026378    .004768     5.53   0.000      .017033     .035723
     indirect_M2 |   .0549647   .0090522     6.07   0.000     .0372228    .0727066
    total_indir~t |   .0813427   .0113735     7.15   0.000     .0590511    .1036344
    
     total_effect |    .381957   .0523959     7.29   0.000     .2792629    .4846511
    Thank you in advance for any insights or recommendations!

  • #2
    I think the most crucial point of the analysis is whether it is valid to estimate the indirect effects by multiplying the coefficients, as in
    Code:
    indirect_M1: _b[M1:X]*_b[Y*M1])
    The first term is the coefficient from the continuous mediator model, the second is the one from the binary outcome model. Usually, these should be both from continuous models (the standard approach, when the outcome is continous).

    Have you tried the KHB approach? I have tested it extensively and believe it is extremely robust, for other, published results see
    https://journals.sagepub.com/doi/pdf...867x1101100306
    https://journals.sagepub.com/doi/10....36867X19893638

    The KHB approach giving results similar to your current ones would be a good sign.
    Best wishes

    Stata 18.0 MP | ORCID | Google Scholar

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