Interpretation moderating variables

[Liselotte Nel]

Hi everyone,

I am doing research on the effect of entrepreneurial behaviour on firm performance and I want to add a moderating variable of corporate culture to it.

I find difficulties with interpreting the results of the moderating effect.

What I did:
reg LNvalSales c.entrepreneurialintentions##c.pdi LNFTTtotal LNage if dr== 1, robust
margins, at(pdi=(-19.43817 19.43817) entrepreneurialintentions=(-4.642227 4.642227))
marginsplot, noci x(entrepreneurialintentions)


The coefficient of the interaction term is -.0055701 and you can find the marginsplot here:



what does these results mean I how do I interpret the marginsplot ?

thank you in advance!

[Daniel Schaefer]

Hi Liselotte,

The answer to this question will likely depend on some details that are unclear. Is pdi your corporate culture variable? Is it continuous, ordinal, categorical, or dichotomous? If it is not continuous, what are the levels of your corporate culture variable, and what do those levels indicate? A data example generated with -dataex- would be very helpful here.

Edit: Setting aside how to interpret the interaction, I think you might have coding problem or two, but again, it's a little difficult to tell without a data example.

[Liselotte Nel]

Hi Daniel,


hereby a data example

pdi is indeed corporate culture. It is a dimension of culture and goes from 0 to 100 (index). Mean is 49.8.
The theory behind it is, when power distance (pdi) is high, thus above 50, entrepreneurial intentions should be diminished.

Is this enough information for you?

[Daniel Schaefer]

Thanks Liselotte,

If you provide the sample data as text rather than as an image I can run stuff locally on my instance of Stata, which is generally very useful.

What you see in the margins plot are predicted values for your outcome (y-axis) for entrepreneurial intentions (x-axis) between -4.642227 and 4.642227. The blue line indicates predicted values where PID = -19.43817 and the red line where PID = 19.43817. Notice that the slope of the relationship between entrepreneurial intentions and your outcome differ for different values of PID. This is what your interaction term is modeling.

However, please note that it doesn't look like negative values are in the domain for either PID or entrepreneurial intentions. This means that you are using your model to predict values for improbable, impossible, or unobserved situations - not a great foundation for meaningful analysis. A good heuristic is to only use values of these two variables that actually make sense given your data when you create your margins plot. When you write your margins command, ask yourself what might constitute interesting values of PID and entrepreneurial intentions, and go from there.

[Liselotte Nel]

Hi Daniel,

I made a mistake in the command, I thought that I was writing minus SD and plus SD but I see now that indeed I write negative value.

If I run the code:
reg LNvalSales c.entrepreneurialintentions##c.pdi LNFTTtotal LNage if dr== 1, robust
sum entrepreneurialintentions
local EI_low = r(mean) - r(sd)
local EI_high = r(mean) + r(sd)
sum pdi
local pdi_low = r(mean) - r(sd)
local pdi_high = r(mean) + r(sd)
margins, at(pdi=(`pdi_low' `pdi_high') entrepreneurialintentions=(`EI_low' `EI_high'))

I get the error "invalid numlist has to few elements". What to do about this?

[Daniel Schaefer]

Hi Liselotte,

I can run the code you provide on example data without an error (Stata 17). Remember that local variables fall out of scope when the code finishes executing, so if you run this (e.g.) one line at a time, by the time you hit the -margins- command your local variables are no longer in the global environment and get interpreted as the empty string. You can display `pid_low' to test this behavior.

You can fix this by highlighting every single line starting with the first -sum- and ending with the -margins- command and clicking the run button. If you run all of these lines at the same time it should work. Alternatively, you could also change these locals to globals or even scalers and they will persist in the environment after execution is complete.

[Liselotte Nel]

Hi Daniel,

it worked!!

Now I have the following plot

how do I interpret it? As follow?
If there is high entrepreneurial intentions and high power distance, there is diminishing effect of entrepreneurial intentions on firm performance. Low power distance has a increasing effect on entrepreneurial intentions.
If there is high entrepreneurial intentions and high power distance, there is diminishing effect of entrepreneurial intentions on firm performance. Low power distance has a increasing effect on entrepreneurial intentions.

Or can I give a more elaborated interpretation of the moderating effect?

[Daniel Schaefer]

Hi Liselotte,

Personally, I might say that for cases with relatively low values of pdi, there is a moderate, positive relationship between entrepreneurial intentions and your outcome, whereas for cases with relatively high values of pdi there is a strong negative relationship between entrepreneurial intentions and your outcome. I might also wonder why, theoretically speaking, it might make sense for the direction of the relationship between entrepreneurial intentions and your outcome to change with respect to different values of pdi. This will likely have a great deal to do with your particular field, but I suspect a clear theoretical understanding of why the degree and direction of the relationship changes as pdi changes will be most productive for you as far as interpretation goes.

[Liselotte Nel]

Hi Daniel,

this is great! Thank you so much for your help!!

Indeed, the theory shows that a high pdi would render entrepreneurial intentions, thus as a moderating effect is would be a negative relationship.

If you do not mind, I have some further questions about my results.
Model 2, regression analysis of EI on firm performance shows a negative coefficient (insignificant). Model 3 regression analysis of EI, PDI and EI x PDI shows a positive coefficient of EI. How is that possible? How can I explain this change?

Also, model 5, regression of EI, MAS and EI x MAS. Direct EI is statistically significant. How can EI be significant in this model and insignificant in the other models?

[Daniel Schaefer]

The variable likely transitions from significant to not significant because of some collinearity among your predictor variables. There is, in effect, some overlapping explanatory power between two or more of your predictor variables.

As for the sign change, I prefer to interpret nonsignificant values as not statistically distinct from zero. The sign of a non significant value isn't really meaningful. I would more or less just take the direction when the variable is significant to be the "true" direction of the relationship.

[Daniel Schaefer]

By the way, did you know you can highlight Stata output, right click, and copy the text as an image? That might be easier than whatever it is you did to get the image above...

[Liselotte Nel]

Allright, thank you so much!