Mediation: Direct effect greater than the Total effect !

[sedki zn]

Dear all,

i hope you are doing good in this period of Covid

in my work i have studied the following relationships:

1. impact of financial constraints on CEO stock option using a threshold model
2. impact of CEO stock option on Risk taking using quantile regression
3. impact of financial constraints on risk taking using threshold model

Now i would study the mediating role of CEO stock option in the relationship between financial constraints and risk taking following The Baron and Kenny (1986) method.

following are the results:

as shown in the tables above, there exist a Partial mediation. but as marked in yellow, the direct effect is found to be greater than the total effect. i get confused how to interpret this. i have find that they call this a "Inconsistent mediation". i am wondering how can i interpret this !! what is the role of the mediator here exactly !!


Kind regards
SEDKI

[sedki zn]

Dear Professor Clyde Schechter,

i would appreciate your help as you always do

kind regards

[Clyde Schechter]

Disclaimer: You don't show what command(s) you used to generate this output. The beginning of it looks like output from -sem- or perhaps -gsem- but the second screen shot is not something I recognize. So I'm going out a limb and making some guesses about what's going on here. It is possible that I do not properly understand what the outputs you show are supposed to mean.

But disregarding the second screenshot and looking only at the SEM output, nothing seems wrong here. Notice that the coefficient of INDEXfcp for outcome RD is negative. This is key to understanding what's going on here.

Now, the indirect effect of INDEXvcp on RD, i.e. along the path mediated by SOTOTREM is 0.0064646*1.743768 = 0.01127276, which corresponds to what the second screenshot shows.

The direct effect of INDEXfcp on RD is -0.0832749, which is negative. This is misreported in the second screenshot, as the minus sign is omitted.

The total effect is the sum of the direct and indirect effects, which is -0.07200214. Since the direct effect is negative, the indirect effect will be larger than the total effect. Notice that this total effect is also misreported in the second screenshot, the negative sign having been omitted again.

So the total effect is the net result of a relatively large negative direct effect, which is slightly offset by a smaller (in magnitude) positive indirect effect through SOTOTREM.

I think that whatever program you used to get the results in #1 has a bug and does not handle negative path coefficients properly.

[sedki zn]

Dear Clyde Schechter

thank you for your reply and sorry for the messing details concerning the model used
yes as u guessed, the first command is "sem" and following the second command

as you mentioned, i am wondering, too, why the negative sign is omitted !!! maybe they use the absolute values ?? or maybe both values are negative so it is the same to take positive values ??

kind regards

[sedki zn]

Dear Clyde Schechter

So the total effect is the net result of a relatively large negative direct effect, which is slightly offset by a smaller (in magnitude) positive indirect effect through SOTOTREM.

so here what is the exact role played by stock option in the relation between financial constraints and R&D ?
it amplifies the negative impact or reduce it ?


kind regards
sedki

[Clyde Schechter]

Sorry, I don't know what you're asking here. You have two explanatory variables, SOTOTREM and INDEXfcp. Which of them, if either, is stock option and which is financial constraints? Those variable names might be recognizable to people who work in your area, but to me they mean nothing at all--I'm an epidemiologist.

[sedki zn]

Sorry, I don't know what you're asking here. You have two explanatory variables, SOTOTREM and INDEXfcp. Which of them, if either, is stock option and which is financial constraints? Those variable names might be recognizable to people who work in your area, but to me they mean nothing at all--I'm an epidemiologist.

Sorry Professor, you are right

stock options is SOTOTRUM = mediator
indexfcp is financial constraints = indep var

I'm asking about the role of the mediator here !

[Clyde Schechter]

The way I would summarize this is:

Financial constraints have a direct negative impact on R&D of moderate magnitude. However, financial constraints also have a small positive impact on stock options. Those stock options, in turn, have a strong positive effect on R&D. Putting it all together, the small positive impact of financial constraints on stock options induces a small positive impact on R&D that is mediated through stock options. This small positive effect somewhat offsets the direct negative impact of financial constraints on R&D. When all is said and done, the net effect of financial constraints on R&D is negative, but not quite as negative as it would be in the absence of the mediating effect of stock options.

[sedki zn]

When all is said and done, the net effect of financial constraints on R&D is negative, but not quite as negative as it would be in the absence of the mediating effect of stock options.

Thank you dear Professor for your very clear answer.
just one more thing. I can understand from this that if the indirect effect was negative ( impact of financial constraints on stock options is negative) then the mediating role of stock options is to amplify the negative relation between financial constraints and R&D?? ( even then impact of stock options on R&D is positive ( direct effect sign ) ????
Because here I really cannot understand if we should compare the values with their signs or no. If so, in the case of the indirect effect is negative added to the negative direct effect in whole we will have a total negative effect greater than the direct effect. This means, stock options reduces the negative impact !!
I'm kinda confused here. ( because in any case of the sign of financial constraints on stock options, this latter with reduce the negative impact of FC on D&D) !

kind regards

[Clyde Schechter]

I can understand from this that if the indirect effect was negative ( impact of financial constraints on stock options is negative) then the mediating role of stock options is to amplify the negative relation between financial constraints and R&D??

I'm not sure what you're getting at here. In fact, the indirect effect of financial constraints is positive. As I noted in #3

Now, the indirect effect of INDEXvcp on RD, i.e. along the path mediated by SOTOTREM is 0.0064646*1.743768 = 0.01127276, ....

Now, perhaps you are asking something like this: imagining a counterfactual situation in which the indirect effect of financial constraints were negative, would that mean that stock options amplify that negative effect? Yes, in that counterfactual situation, the effect of stock options would be to amplify the negative direct effect of financial constraints on R&D.

But in the actual situation, the mediation of stock options slightly reduces the negative direct effect of financial constraints.

[sedki zn]

Dear Clyde Schechter

thank you very much
I really do appreciate your time

kind regards

[sedki zn]

Dear Clyde Schechter

sorry for bothering again.

i am wondering how the results of this output are correct ! it is mentioned that the Sobel test is not significant ( so the indirect effect) but there exist a partial mediation ! how this could be possible ??

Kind regards
Sedki

[Clyde Schechter]

Well, as I indicated above, I am not familiar with the -medsem- command. My interpretations of the results have all come from the -sem- output. I think we have already seen that the -medsem- output is incorrect in its handling of negative effects. So it wouldn't surprise me if other aspects of it are incorrect as well. Frankly, I don't think I would use -medsem-; it does not appear to be reliable. -sem- and -estat teffects- do not organize the output in the neat way that -medsem- does, but well-organized incorrect results are not useful.

I would run -sem- and -estat teffects- on your data. The Sobel test is just looking at the p-value of the indirect effect. As in other contexts, I de-emphasize p-values and statistical significance, but you can look at the indirect effect of INDEXfcp on RD (coefficient, and confidence interval) and draw your conclusions about whether there is a meaningful mediation here or not.

[sedki zn]

Dear Clyde Schechter

i have tried the mediation through a threshold regression. following are the results
i tried to follow the same logic as through linear mediation to interpret the results but somehow i got lost !

1: x (financial constraints) ----->y (R&D)

2: x -------> M (SO)

3: X M -------> Y

as mentioned in the three tables;
1: the total effect (x-->Y) is negative below and above the threshold value.
2: the effect of FCP index on SO is positive (negative) below (above) the threshold value financial constraints.
3: concerning the direct effect, it remains negative below and above but it has decreased. the SO is shown to be positive.

here if we put all together, the negative impact of financial constraints on R&D has decreased due to the positive impact of SO on R&D ?? or should i interpret the results based on the impact of Financial constraints on SO below and above the threshold value !? if so, the interpretation would be; Stock options reduce the negative impact below the threshold variable and increase it above ??
it seems a bit complicated to me.

i would appreciate your help

kind regards

[Clyde Schechter]

Well, your confusion is contagious. I'm confused, too. You are showing outputs in a way that I am having difficulty following. First of all, now we have new variables SA and KZ index that have not been mentioned before. So what are these about? Also, there is no output shown for M--->Y, which is something I look at when trying to interpret mediation models. Can you just run these analyses in SEM and show the Stata output from that? I'm much more comfortable interpreting that.