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

[Emily Soriano]

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>