Interpreting significant interaction effect while main effect is insignificant

[Eline Meijer]

Hi!

I am investigating the effect of balanced ambidexterity and combined ambidexterity on firm performance, with moderating variables environmental dynamism and environmental munificence.
While my main relation is insignificant, the interaction effect of my moderating variable is significiant.
How do I need to interpret this, and can I give support to the proposed hypothesis of a positive moderating effect if the main effect is insiginificant?

Note: for the moderating variables, variable * BD or variable * CD stands for interaction term with m

 
**Dependent:
			 Sales Growth 3 year
			Model
			0
			Model 1
			Model
			2
			Model
			3
			Model
			4
			Model
			5
			Model
			6
			Model
			7
			Model
			8

Independent variable 










Balanced Ambidexterity 

			-.348

			-.358

			0.044

			.049


Combined Ambidexterity 


			.019

			.024

			.016

			.014

Moderator variables










Environmental Dynamism 
			 
			Environmental Dynamism * balanced ambidexterity 
			 
			Environmental Dynamism * combined ambidexterity 



			-0.862
			 
			-.195
			-1.090
			 
			 
			 
			 
			 
			.053


			-1.244
			 
			.065
			-1.223
			 
			 
			 
			 
			 
			0.032

Environmental Munificence 
			 
			Environmental Munificence * Balanced Ambidexterity 
			 
			Environmental Munificence * Combined ambidexterity





			30.155**
			 
			 
			3.951**
			34.137**
			 
			 
			 
			 
			 
			1.135**
			30.145**
			 
			 
			4.054**
			34.193**
			 
			 
			 
			 
			 
			1.179**

Control variables










Exploration 
-.287
.052
-.469
-.063
-.483
-.383
-.512
-.395
-.521

Exploitation 
 .036
.388
.023
 .450
-.024
-.042
.014
-.551
.013[EM1]

Industry type 
-.424**
-.424**
-.420**
 -.398**
-0.394**
-.212*
-.229**
-.186**
-.202**

Firm size 
-.342**
-.342**
-.340**
-.339**
-.338**
-.296**
-.302**
-.295**
-.300**

Firm age 
-.035**
-.035**
-.036**
-.035**
-.035**
-.315**
-.035**
-.032**
-.032**

Year dummies
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Observations
2412
2412
2412
2412
2412
2412
2412
2412
4212

Number of firms
402
402
402
402
402
402
402
402
402

Wald Chi-square
38.21
 32.83
32.04
32.89
32.90
89.25
130.12
88.71
128.16

Log-likelihood










P > Chi-square
0.000**
0.000**
0.000**
0.000**
0.000**
0.000**
0.000**
0.000**
0.000**

**. is significant at the 0.05 level. *. is significant at the 0.10 level.
			Year dummies are not reported.






    

THanks in advance!

Eline

[Maxence Morlet]

I don't know moderation analysis very wel, but in a normal, linear regression setting, Suppose you include in a Mincerian regression female, age, and the interaction between the two.

Suppose female and age are individually insignificant; they do not significantly affect wages. But their interaction is significant and positive (this is all hypothetical). This means that for females, an additional year of age increases wages by more than for the base group (presumably males).

[Richard Williams]

This might help. The interpretation of main effects changes when interaction terms are added.

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

[Maxence Morlet]

Exactly like Richard said, in my example, the coefficient on age would reflect the impact of one additional year of age on earnings for males.

[John Kane]

Hi Eline,

A couple quick things that might help:

1) Note that, in any interaction analysis, you need to estimate coefficients on the constitutive terms for any interaction you specify. For example, in Model 5, it looks like there are two interactions: 1) EM * Balanced, and 2) EM * Combined. However, there is only a coefficient (.044) on one constitutive term ("Balanced") whereas there needs to be one on 1) balanced, 2) combined, and 3) EM. Again, there must be a coefficient on each individual term that is contained within any interaction, otherwise the coefficients in the interaction become essentially meaningless.

2) Assuming that the model is specified correctly, we'll take the "30.155" coefficient in Model 5 as an example. What this tells you is how much the effect of balanced dexterity (on sales growth (Y)) changes given a one-unit increase in EM. Put differently, the slope of balanced dexterity on Y gets significantly more steep as EM increases. If the coefficient on balanced dexterity is already positive (which it is), then this interaction tells you that the effect is getting stronger as EM increases.

Again, point #1 can't be emphasized strongly enough before thinking about point #2.

Hope this helps!

[Joro Kolev]

Neither the main effect, nor the interaction term, have a meaning on their own. You need to consider the whole derivative.

E.g., in
EY = a + b*X + c*X*Z + d*Z

d(EY)/dX = b + c*Z

If you want to know whether X impacts EY you need to consider b + c*Z as a whole, not the main effect in isolation, and not the interaction term in isolation.