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I ran mediation analyses with Lavaan (using 5000 iterations bootstrapping). My model is a simple mediation model where M mediates the relationship between X and Y. But there is also a moderator (Mod) that influences the relationship between X and M and between X and Y.

Looking at the results, I get the following:

Regressions:
               Estimate  Std.Err  Z-value  P(>|z|)
 Y ~                                               
  X  (c1)   -0.017    0.008   -2.116    0.034
  Mod (c2)   -9.613    3.655   -2.630    0.009
  X*Mod (c3)    0.017    0.007    2.475    0.013
 M ~                                          
  X  (a1)    0.003    0.002    1.463    0.143
  covariate1           0.004    0.003    1.564    0.118
  covariate2               0.038    0.028    1.387    0.165
  covariate3           0.004    0.004    1.053    0.293
  Mod  (a2)    1.874    0.972    1.927    0.054
  X*Mod (a3)   -0.003    0.002   -1.766    0.077
Y ~                                               
 Mod  (b1)   -0.892    0.437   -2.040    0.041
 covariate1          -0.007    0.014   -0.486    0.627
 covariate2               0.600    0.156    3.850    0.000
 covariate3           0.059    0.027    2.195    0.028

Variances:
               Estimate  Std.Err  Z-value  P(>|z|)
 Y               0.593    0.073    8.142    0.000
 M          0.021    0.005    4.563    0.000

Defined Parameters (conditional effects at different levels of Mod):
               Estimate  Std.Err  Z-value  P(>|z|)
directXM1          -0.000    0.000   -1.129    0.259
directXM2           -0.001    0.000   -2.646    0.008
directXM3         -0.001    0.000   -2.846    0.004
indirectXY1           0.000    0.000    1.017    0.309
indirectXY2           0.001    0.000    1.784    0.074
indirectXY3          0.001    0.001    1.703    0.089
directXY1           0.001    0.002    0.381    0.703
directXY2            0.003    0.001    1.951    0.051
directXY3          0.005    0.002    2.974    0.003

I notice that the X*Mod on M (a3) is not significant (p = 0.077), but the confidence interval for this [-0.008, -0.001] (confidence interval comes from the bootstrapped results) Furthermore, I also noticed that the indirect effect is not significant (at any levels of the moderator).

How should I interpret this? I was thinking of removing XMod on M from the model... but then 0.07 is not that far from significant (and looking at the CI...)? The indirect effect is not significant... When I remove this interaction (XMod on M) and calculate the indirect effect as a1*b1, the indirect effect is even less significant (p=0.104). I am totally lost on what it means that the indirect effect is not significant. Does that mean that there is no real mediation effect?

Many thanks! Best H

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