# partial mediation Or no effect

I did the mediation analysis for my research using SPSS (linear regression) between internal career opportunity as (IV), social exchange as (MV) and organisational performance as (DV), and I followed Baron and Kenny Method.

And I got these results as you can see in the table below.

In the first step (path c), a crucial relationship between the outcome and the predictor is shown without the mediator and it was found that IV was significant as their p-values are less than 0.05 (p < 0.05).

In the second step(path a), the predictor and mediator’s relationship is established. The results for the second step are presented in the table below. Hence, the first and second conditions were met of Baron and Kenny Method.

Third Step and step four is run together: In the third step (path b), the mediator (social exchange) and outcome variable’s (OP) relationship is shown. The result of the third step in the below table shows that the impact of (MV) on the (DV) is significant, having the p < 0.05 hence confirming the third step but the result in fourth step(path c’) shows that after including MV in the equation, the IV remain significant with (p < 0.05). This being the remaining significance, after introducing the mediator in the model showing the partial mediation. The condition for the full mediation is for the predictors to be insignificant when the mediator is introduced.

My question is when we have significant in step 1 and step 2 and 3 but no change in results for step4 (bath c' )..... What is this called? Do we call this "Partial Meditation"? or something else?

• You may well be right that it is "partial mediation". But take this comment and use it to edit your question. Also, talk about effects (coefficients), not just p-values. Talk about your design too. Lay out the information like these in a methodological manner. I think I know what (a) and (b) and (c') mean but these are just things in psychology-related fields. The larger statistics community is unlikely to have an idea what these things mean. – Heteroskedastic Jim Sep 28 '18 at 16:16
• Thank you so much for your piece of advice. So, even if we don't have any effect in the result after introducing the mediator still can be called “partial mediation”?. As you can see (step 1 and step 4 same results). – Tam Sep 28 '18 at 18:47

The general framework for mediation analysis is to run three models:

• Model 1: a * IV -> DV (to establish some kind of total effect)
• Model 2: b * IV -> MV (to establish some effect on the mediator)
• Model 3: c * IV + d * MV -> DV

where a to d stand for regression coefficients.

The first thing to check for in mediation is evidence of an indirect effect of A on C. The path for that is b (from IV to MV) multiplied by d (from MV to DV with IV in the model). If there is no indirect effect, there is no mediation. If b * d is not statistically significant, then there is not sufficient evidence to detect the mediation effect. I will call b * d, ie for indirect effect: $$ie = b \times d$$.

Because ie comes from two models, models 2 and 3, we need some method to test whether it is statistically significant. The more traditional approach is the Sobel test, which is just a specialized form of the delta method, which is a first order Taylor Series expansion. The assumption built into this method is the normality of ie. You will often need a large sample size for this assumption to be satisfied. So these days, it is more common to perform bootstrapping. Within each resample, retrieve b and d from Models 2 and 3 respectively, multiply them to get ie, and obtain the confidence interval for ie at the end. Since you use SPSS, there is a macro called Process that implements bootstrapping for the indirect effect.

So if your indirect effect is not statistically significant, you can end your talk of mediation.

If it is statistically significant, it is also reasonable to expect that a in Model 1 would be statistically significant, suggesting evidence of a total effect. The same goes for b suggesting that a at least influences your mediator. Also d suggesting that your mediator influences the outcome. The question then becomes: which type of mediation do you have: partial or complete?

Here's the standard approach:

• If c is statistically significant in the presence of an indirect effect, then the relationship from the IV to the DV persists in the presence of the mediation effect, so we only have partial mediation.
• If c is not statistically significant in the presence of an indirect effect, then the relationship from the IV to the DV vanishes in the presence of the mediation effect, so we have complete mediation.

In your particular situation, I do not see the indirect effect, so it is difficult to begin the conversation about mediation. I will assume that your Steps 3 and 4 are my Model 3. If that is true, then $$b=.435$$ and $$d=.231$$, so it is possible to conduct the Sobel test.

With the Sobel test, the formula for the standard error of the indirect effect is: $$\sqrt{b^2 \times se_{d}^2 + d^2 \times se_{b}^2}$$ In your case, $$se_d = d/t_d= .231/2.484=0.092995$$ and $$se_b = b/t_b= .435/4.4=0.09886$$. So the standard error of your indirect effect is: $$\sqrt{.435^2 \times 0.092995^2 + .231^2 \times 0.09886^2}=0.04645$$ Your indirect effect will be: $$.435\times .231=0.100$$. So your $$t$$-statistic for the indirect effect will be $$.1/.04645=2.15$$.

I hope this helps. Personally, I doubt the results of mediation analyses. I think it is a causal analysis, so when estimated using ordinary least squares (as you are doing), it is plagued by omitted variable bias. So I do not believe any of these results generally.

• If the reply answers your question, you can mark the reply as accepted. And you're welcome. – Heteroskedastic Jim Sep 29 '18 at 18:38