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I am running a model of the following form:

lm(outcome ~ treatment) in which I cluster standard errors at the participant level.

I ask respondents at the end of the treatment a laundry list of affective questions (about 20) about their experience in the experiment and those involved. Many of these questions are highly collinear with each other. I want to see which of these variables potentially "mediates" the relationship between the treatment and outcome.

Is there an algorithmic solution for sorting through a large list of potential mediators (and their interactions with other potential mediators) to find candidates?

What are the state of the art mediation techniques?

To clarify: I'm using

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One way to assess multiple mediators in an exploratory fashion is regularized mediation, which is described by Serang et al. (2017). It uses lasso to select the paths from the predictor to the mediators and from the mediators to the outcome. Any potential mediator for which either path is selected out is considered not a mediator, and potential mediators with nonzero paths are retained as mediators. Once they have been chosen, the mediation model is refit with the selected mediators.

Note that this method relies on the linear structural equations modeling formulation of mediation, which has limitations and may not truly represent the data-generating model. Causal mediation approaches are more robust and flexible, but I don't think variable selection has been implemented in them yet.

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  • $\begingroup$ This is helpful, but I don't use structural equation modeling. I'm using a standard linear regression with robust standard errors. Any ideas on that front? $\endgroup$
    – Parseltongue
    Commented Jul 20, 2019 at 1:59
  • $\begingroup$ You have to use SEM or specialized mediation tool to perform mediation. Generally, you can't perform variable selection and inference at the same time in the same dataset, so decide if you want your analysis to be exploratory or confirmatory or split your dataset into two. If you want variable selection in mediation, my answer is the only way that I know of. Consult with a quantitative psychologist if you don't understand SEM, but don't avoid using it just because you haven't learned about it yet. $\endgroup$
    – Noah
    Commented Jul 20, 2019 at 7:04
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    $\begingroup$ Also, SEM, as I'm recommending it, is just a series of simultaneous linear regression models. There are no additional interpretational difficulties. I'm not recommending a latent variable model (although that might answer your research question better). $\endgroup$
    – Noah
    Commented Jul 20, 2019 at 7:05
  • $\begingroup$ Thanks, Noah. I'll look into this! $\endgroup$
    – Parseltongue
    Commented Jul 21, 2019 at 3:02

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