[Mediation-information] Question re: non-linear outcomes

[Kentaro Hirose]

Hi Emily,

Since you are using a logit model, the total effect (0.02) is estimated
based on the probability scale, and this is different from the coefficient
(0.30) estimated in the logit model.

Best,
Kentaro

2016-11-16 22:03 GMT+09:00 Emily Soriano <esoriano at psych.udel.edu>:

> Hello,
> I am a third year doctoral student in clinical psychology at the
> University of Delaware currently working with causal mediation analysis in
> R. I want to thank you very much for your contributions to the field and
> for making this very useful tool, along with many helpful resources, freely
> available. I am hoping to clarify a two questions I've encountered using
> your R package with my data. I apologize for the length of this email, but
> I wanted to provide all relevant details. First, some background:
> I am examining a 1-1-1 multilevel mediation model using daily diary data
> completed by a sample of breast cancer patients.
> X = peNEcs = continuous, sum of daily negative events (each event coded 0
> (didn't occur) or 1 (did occur)), measured at the daily level
> Mediator = peFORs = count distribution, fear of cancer recurrence,
> measured at the daily level
> Y = check = binary, checking behavior (single item coded 0 (no, did not
> check today) or 1 (yes, did check today), measured at the daily level
> In addition to the raw variables (above), the person means are also
> included as person-level covariates (peNEcgmc, peFORgmc). Time
> (DiaryDaygmc) is included in all models as a daily level covariate.
> All the relevant input/output from R can be viewed here:
> https://www.dropbox.com/s/si4o8wz8yk6btj6/R%20input%20output.docx?dl=0
> Question 1: I am having difficulty making sense of how the estimates of
> the causal mediation analysis are scaled. I have read that these estimates
> should be on the same scale as the outcome - which, in this case, is log
> odds. However, estimates of the total effect and average ACME and ADE, if
> in log odds units, do not correspond to and in fact are much smaller than
> results from the preliminary regression models. While I expect the
> estimates to be slightly different, these estimates are different enough to
> make interpretation difficult.
> For example, the estimate of the total effect (X-->Y) from the regression
> model is 0.3006 (in log odd units):
> > totalef <- glmer(check ~ peNEcs + peNEcgmc + DiaryDaygmc +
> (1|ï..CoupleID), family = binomial(link="logit"), data=syp)
> Fixed effects:
>              Estimate Std. Error z value Pr(>|z|)
> (Intercept) -2.592114   0.309711  -8.369  < 2e-16 ***
> peNEcs       0.300601   0.114772   2.619  0.00882 **
> peNEcgmc     0.376437   0.326597   1.153  0.24907
> DiaryDaygmc  0.006354   0.014695   0.432  0.66548
> ---
> However, the total effect estimate from the mediation analysis is 0.02231:
> > multimed <- mediate(model.m, model.y, treat="peNEcs", mediator="peFORs",
> sims = 1000, control.value=0, treat.value=1, dropobs = TRUE)
> Total Effect              0.02231     -0.00232      0.04899    0.08
> ACME (average)            0.01278      0.00636      0.02174    0.00
> ADE (average)             0.00953     -0.01536      0.03565    0.43
> Prop. Mediated (average)  0.55048     -2.00847      3.60052    0.08
> There are similar patterns of divergence for the ACME and ADE as well.
> Using a control value of 0 and treat value of 1 in the mediate command, I
> believe, should allow for comparable (although not exact) estimates for the
> total effect estimate from 'mediate' and the slope estimate from the
> multilevel regression. If those estimates are on the same scale (log odds),
> then I would greatly appreciate any guidance about how to understand and
> interpret such attenuated effects via the causal mediation analysis. The
> relative size of the ACME does seem in line with our initial regression
> results, it is just the scale that I'm having trouble making sense of.
> Question 2: In addition, I hoped to clarify the recommended approach for
> using a continuous x in this framework. From my reading of your work in
> this area (e.g., Imai, Keele, & Tingley, 2010), I gather that the
> recommended approach is to run a series of 'mediate' commands, starting
> with control value = 0, treat value = 1, then control value = 1, treat
> value = 2, etc. Then one can plot the ACME estimates from the different
> treat/control values, and also obtain an average estimate across the
> different treat/control values. Am I getting this right? Do you have any
> additional recommendations for working with, interpreting, and reporting on
> the ACME with a continuous X?
> Thank you very much in advance for you time and assistance.
> Emily Soriano, M.A.
> University of Delaware
> Department of Psychological & Brain Sciences
> 302-831-8188
> esoriano at psych.udel.edu<mailto:esoriano at psych.udel.edu>
>
>
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