# Is there evidence of mediation? Need help with interpretation of mediation analysis results

I have performed a mediation analysis. I have an independent variable T, a mediator M, and outcome Y. (All 3 variables are binary, and I use logit.) (While I used Stata medeff command to run the mediation analysis, this is NOT a question about medeff.)

(I make reference to the standard mediation triangle, where path a connects T and M, path b connects M and Y, and path c' connects T and Y.)

Equation 1 is simply regressing M on T and some control variables. (this gives an estimate for path a) Equation 2 regresses Y on M + T +control variables. (this gives estimates for b and c')

What I find is the following:

I get a significant negative association between T and M. (path a) I get a significant positive association between T and Y. (path c') I get a "non-significant" association between M and Y (path b)

Equation 1
M       Coef.   Std. Err.        z    P>z   [95% Conf.  Interval]
T   -3.458955   .1044635    -33.11  0.000   -3.6637 -3.25421

Equation 2
Y       Coef.   Std. Err.       z     P>z   [95% Conf.  Interval]
T    .6081007   .0949606     6.40   0.000   .4219813    .7942201
M   -.1496489   .0989504    -1.51   0.130   -.3435881   .0442904


So, path a is significant and negative, path b is not significant, and path c' is positive and significant. Based on that, from what I understand from Baron and Kenny 4 steps, I would conclude that there is no mediation because path b is not significant. However, medeff produces the following results:

==========================================================
Effect                   Mean       [95% Conf. Interval]
ACME1                   .0189176   -.005018      .0438004
ACME0                   .0160403   -.0041128     .0379756
Direct Effect 1         .1274808    .0903369     .1646811
Direct Effect 0         .1246035    .0863965     .1633032
Total Effect            .1435211    .1134255     .1722113
% of Total via ACME1    .1313853    .1098513     .1667854
% of Total via ACME0    .1114022    .0931433     .141418
Average Mediation       .017479    -.0045654     .0409513
Average Direct Effect   .1260421    .088528      .1640466
% of Tot Eff mediated   .1213937    .1014973     .1541017
============================================================


So, medeff says there is 12% mediation by M (looking at the last row, % of Total Effect mediated.)

So, my questions are:

1. Given the results from the two regression analysis above, should I ignore the medeff results and conclude that there is no mediation? Or is there actually mediation?
2. Why if medeff says that there is 12% mediation, would the confidence interval for "average mediation" include 0, ie not significant?
3. Is it enough to simply report the % of total effect mediated? or do I also have to report average mediation?
• Cosmetic, but never say that you have a simple question. It's unnecessary if you're right that it's simple, yet puzzling if you're wrong. Also, although people won't usually say so, it invites the rhetorical response that if that's simple, why are you asking? – Nick Cox Nov 14 '14 at 18:08
• I see, I used Stata's medeff function, which can implement causal mediation analysis for non-linear systems (ie, binary outcome) – taraj Nov 14 '14 at 18:12
• Cross-posted at statalist.org/forums/forum/general-stata-discussion/general/… Policy on CV resembles that on Statalist that cross-posting is in order, but you should be open about it. – Nick Cox Nov 14 '14 at 18:15
• yes, apologies, I did not know. Will do so in future posts. thank you. – taraj Nov 14 '14 at 18:21