I have 3 variables which I used to conduct a mediation analysis. Since it is unclear to me whether which variable should be the (in)dependent variable and which should be mediator, I constructed 3 models. Using package mediation
, I got the results which show all three models are statistically significant:
Model 1:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 54.0422 4.7155 11.460 < 2e-16 ***
X 27.5089 9.9512 2.764 0.00747 **
M 0.9369 0.4571 2.050 0.04455 *
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 7.2197 0.8546 17.56 0.022 *
ADE 27.5089 11.1184 44.51 <2e-16 ***
Total Effect 34.7285 19.1319 53.34 <2e-16 ***
Prop. Mediated 0.2079 0.0292 0.54 0.022 *
---
Model 2:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 54.0422 4.7155 11.460 < 2e-16 ***
X 0.9369 0.4571 2.050 0.04455 *
M 27.5089 9.9512 2.764 0.00747 **
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.447 0.141 0.78 0.002 **
ADE 0.937 0.153 1.89 0.014 *
Total Effect 1.384 0.544 2.37 <2e-16 ***
Prop. Mediated 0.323 0.114 0.80 0.002 **
---
Model 3:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.158881 0.096979 -1.638 0.10635
X 0.010813 0.005477 1.974 0.05274 .
M 0.003932 0.001423 2.764 0.00747 **
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 5.44e-03 1.15e-03 0.01 0.006 **
ADE 1.08e-02 -7.11e-05 0.02 0.052 .
Total Effect 1.63e-02 7.09e-03 0.02 0.004 **
Prop. Mediated 3.35e-01 6.56e-02 0.97 0.010 **
---
By quickly looking at ACME and also the p value for M, I would say model 2 and 3 appear to be superior than model 1. Also, for model 3, the X-->Y path was significant before the mediation effect was accounted for and no longer significant after, which isn't the case for model 2. That tells me that perhaps model 3 explains the data the best. However, is that evaluation sufficient? So my question is whether there is a way to statistically evaluate/compare these three models and pick out the one that best fits the data. I thought I'd try lavaan
but from what I can see I can use it to run models with multiple mediators so not what I'm trying to do here. Any advice?