[Mediation-information] Counterintuitive results

[Kentaro Hirose]

Hi Angel, 

To rephrase your question, "why do I get a negative total effect of the treatment on the outcome even though the mediator has a positive effect in the outcome regression model?" 

If this is your question, we also need to know the effect of the treatment on the mediator. If this is negative, then everything makes sense: [1] T has a negative effect on M, [2] M has a positive effect on Y,  and [3] T has a negative direct effect on Y as shown in the second table; If so, T would have a negative total effect on Y.  

Best,
Kentaro



________________________________________
From: mediation-information-bounces at r-forge.wu-wien.ac.at [mediation-information-bounces at r-forge.wu-wien.ac.at] on behalf of Angel Rodriguez [angel.rodriguez at matiainstituto.net]
Sent: Wednesday, September 24, 2014 7:27 AM
To: mediation-information at r-forge.wu-wien.ac.at
Subject: [Mediation-information] Counterintuitive results

Dear Subscribers,

I've carried out the following model:

> library("sandwich")
> set.seed(2014)
> med.fit <- glm(estuprimas ~ edad_c + sexo + regalf + deprinf, family="binomial" ,data=child65)
> out.fit <- glm(benvii ~ edad_c + sexo + regalf + deprinf + estuprimas, family="binomial" ,data=child65)
> med.out <- mediate(med.fit, out.fit, treat = "deprinf", mediator = "estuprimas", robustSE = TRUE, sims=1000, control.value = "no", treat.value = "s\xed")
> summary(med.out)

Causal Mediation Analysis

Quasi-Bayesian Confidence Intervals

                          Estimate 95% CI Lower 95% CI Upper p-value
ACME (control)           -0.012543    -0.029801     0.000732    0.07
ACME (treated)           -0.011498    -0.027808     0.000723    0.07
ADE (control)            -0.049137    -0.125894     0.031768    0.27
ADE (treated)            -0.048092    -0.121987     0.031410    0.27
Total Effect             -0.060635    -0.137208     0.021339    0.15
Prop. Mediated (control)  0.169334    -0.848191     1.686179    0.21
Prop. Mediated (treated)  0.147997    -0.854962     1.689611    0.21
ACME (average)           -0.012021    -0.028888     0.000728    0.07
ADE (average)            -0.048615    -0.124610     0.031589    0.27
Prop. Mediated (average)  0.158665    -0.851577     1.687895    0.21

Sample Size Used: 657

Simulations: 1000


If I understand well, this means that, of the total association of having experienced infant deprivation vs not having experienced it (variable deprinf) on having aged well (-0.06 (OR=0.94; CI95%= 0.87-1.02)) , 15.9% is via the mediator having primary education or more vs less than primary education (estuprimas). This does not make sense to me, because having primary education or more is a protective factor for aging well, as you can see in this model:

Call:
glm(formula = benvii ~ edad_c + sexo + regalf + deprinf + estuprimas,
    family = "binomial", data = child65)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-1.6054  -0.8433  -0.5597   1.0327   2.6291

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  7.29876    1.20323   6.066 1.31e-09 ***
edad_c      -0.10262    0.01619  -6.339 2.31e-10 ***
sexomujer   -0.89359    0.18639  -4.794 1.63e-06 ***
regalfMedia -0.63054    0.27055  -2.331  0.01977 *
regalfBaja  -0.71116    0.23645  -3.008  0.00263 **
deprinfsí   -0.29268    0.23603  -1.240  0.21497
estuprimas   0.33773    0.18910   1.786  0.07411 .


I'd appreciate some insight into this result.

Thank you very much.

Angel Rodríguez-Laso