Interpreting interaction terms

[Rachel Vos]

Good evening!

I have some trouble interpreting my results. Maybe anyone can help.

I have conducted a moderation analysis, with four interaction terms.

Whenever I add one moderator, the IV and the interaction term are highly significant. Whenever I include all moderators at the same time (as it's culture related). The effect of the IV becomes insignificant, as well as 2 of the interaction terms. How can I interpret this?

My supervisor said the results of the moderators tested one by one are the most valuable, but I'm unsure what to do with the IV.

ROA	(2) ESGPDI	(3) ESGIDV	(4) ESGMAS	(5) ESGUAI	(2, 3, 4, 5) FULL INTERACTION
ESG	0.321*** (0.095)	-0.0246*** (0.075)	0.257** (0.104)	0.349*** (0.087)	0.147 (0.287)
AGE	0.022*** (0.003)	0.023*** (0.003)	0.022*** (0.003)	0.023*** (0.003)	0.023*** (0.003)
RISK	0.096*** (0.007)	0.097*** (0.007)	0.096*** (0.007)	0.097*** (0.007)	0.096 (0.007)***
SIZE	0.897*** (0.09)	0.901*** (0.09)	0.896*** (0.09)	0.902*** (0.09)	0.898*** (0.09)
2015	-0.824*** (0.164)	-0.821*** (0.164)	-0.828*** (0.164)	-0.826*** (0.164)	-0.828*** (0.164)
2016	-0.939*** (0.147)	-0.942*** (0.147)	-0.937*** (0.147)	-0.944*** (0.147)	-0.95*** (0.147)
2017	1.34 (0.119)	1.236*** (0.134)	1.245*** (0.133)	1.24*** (0.134)	1.226*** (0.134)
2018	0.011 (0.01)	0.003 (0.119)	0.01 (0.119)	0.002*** (0.119)	-0.008 (0.119)
PDI	0.013*** (0.006)	0.006*** (0.01)	0.005 (0.01)	0.008 (0.01)	0.007 (0.011)
IDV	-0.031*** (0.006)	-0.036*** (0.006)	-0.034*** (0.006)	-0.032*** (0.006)	-0.035*** (0.007)
MAS	-0.017*** (0.006)	-0.016*** (0.006)	-0.011* (0.006)	-0.015*** (0.006)	-0.01 (0.007)
UAI	-0.023*** (0.005)	-0.024*** (0.005)	-0.024** (0.005)	-0.019*** (0.005)	-0.021*** (0.006)
ESGPDI	-0.0068*** (0.002)				0 (0.003)
ESGIDV		0.004*** (0.001)			0.003* (0.003)
ESGMAS			-0.003*** (0.002)		-0.003* (0.002)
ESGUAI				-0.005*** (0.001)	-0.002 (0.002)

[Clyde Schechter]

I cannot tell from your table what the "FULL INTERACTION" model is. And I'm not entirely sure I understand models (2)-(5) either, though I think I do. Please post back showing the exact code that generated each of these models. Also if ESGPDI, ESGIDV, ESGMAS, and ESGUAI are variables you created yourself to represent the interactions (as opposed to letting Stata create them automatically for you using factor-variable notation) please show the code that created those as well.

[Carlo Lazzaro]

Rachel:
in addition to Clyde's concerns (that I share), I would add the following comments:
1) did you use -xtreg- or -regress-?
2) did you test whether the squared term for -age- makes sense as a predictor. If not, please use -fvvarlist- notation, as Clyde wisely suggested:

c.age##c.age

3) why not following the FAQ and use CODE delimiters to share what you typed and what Stata gave you back? Thanks.

[Richard Williams]

I'm guessing that ESGPDI = ESG * PDI, ESGIDV = ESG * IDV, etc. Given your reference to culture, I wonder if PDI, IDV, etc are dummies you created yourself from a multicategory Culture variable. Rather than compute so many terms yourself you would be better off using factor variable notation.

When you compute so many interactions involving the same variable (in this case ESG) they will tend to be correlated, which makes it harder for each one individually to be significant. You may have to choose one. This might be especially good if PDI & IDV etc. were culture dummies. So, for example, you might just use a dummy for the United States (or whatever) if you felt that its culture most differed from the others. Or, alternatively, you might test all 4 interactions collectively rather than one by one.

Once you have interactions, you shouldn't worry too much about the significance of main effects of the variables used to compute the interaction. Their interpretation is different now. See

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

Again, we all are sort of guessing what you are doing, and we may be guessing wrong. If you provide the clarifications requested we may be able to advise you better.