Interpretation of interaction term

[Alex Mayer]

Hallo everyone,

I need help in the interpretation of my interaction term.

Firstly, the setting of my analysis is: Y (dummy) as DV, X (dummy) and interaction term between Z (continous variable) and X as IVs.

My predictions/hypotheses are that
(1) X increases the likelihood for Y.
(2) the positive effect of X on the likelihood for Y is stronger the higher Z is.

Results:

Pr(Y)
X	-0.152***
Z	-0.00914**
X*Z	0.00754*

However with my results, I have to reject my (1) hypothesis -> X decreases the likelihood for Y.

For my (2) hypothesis, the interaction term has a positive sign as predicted.
with margins, dydx (X) at (Z==(-12.0(0.5)+4.5)) I construct this:

However as X is negative, how can I interpret this result?

My attempt of interpretation:
As shown with hypothesis (1), X has a negative impact on Y. So there is no positive effect of X on Y that could be increased by another attribute. However, a higher Z does weaken the negative marginal effect of X on Y. Thus, it positively increases the impact of X on the likelihood of Y if Z is higher, although X still has an adverse impact on that likelihood, even for those with the highest measured Z. As this is in line with the intention of this hypothesis that a higher Z increases the likelihood of Y after X, hypothesis (2) can be partly confirmed.


As I am not sure whether my interpretation sounds correctly, I have following questions:

(1) Is my interpretation of the interaction term and of my (2) hypothesis correct or how can it be improved?
(2) If I am interested in the interaction term of X and Z, do I have to include Z as IV or is it a control variable?

Thank you very much for your help! I really appreciate it!

Alexander Mayer

[Richard Williams]

Once you have an interaction term the main effects can become meaningless. When Z = 0, the predicted value of Y is Bx + Constant. But Z may never equal zero.

Put another way, the effect of X is Bx + BxzXZ = -.152X + .00754XZ. When Z is about 2 or greater, the effect of X is positive.

For more, see

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

[Alex Mayer]

Thank you very much for your reply, Mr. Williams!

Unfortunately, I do not understand how effect of X can be positive when Z>2, as still -.152*1 + .00754*1*2 = -.13692.
As you can see in the graph, for every Z the effect of X is still negative.

So, does it mean that my interpretation is on the right path?

[Richard Williams]

Whoops, I should have said 20, not 2.

But, I still may not like your interpretation. What is the effect of X when there is no interaction? What is the observed and possible range of Z?

Also your graph does show that the marginal effect of X does eventually become positive.

[Alex Mayer]

The effect of X without interaction is negative.
Z can only take values between -12 and 4.5.
As such, the value of the interaction term is "always" negative. However, X*Z is closer to 0 the higher Z.

[Richard Williams]

OK, I was misreading your graph. The Z axis is labeled at the top of the graph rather than the bottom. Given that you get a negative effect of X even without an interaction, your explanation is sounding more reasonable to me.

My phrasings might be more like

(1) Increases in X decrease the probability that Y = 1.
(2) the negative effect of X on the Pr(Y=1) decreases as Z increases.

[Alex Mayer]

So, my interpretation does sound correctly?

Thank you for your time and help, Mr. Williams!

[Eddie Pengma]

Dear Richard,

Thank you for reading and I try to duplicate the results that you attached in the files about interactions, i.e.Appendix: Marginal Effects and Confidence Intervals. But I failed to draw the graph. The stata shows the following:


quietly regress drink gpa male i.male#c.gpa

quietly margins r.male, at(gpa=(0.(.2)4))

marginsplot, scheme(sj) ytitle(predicted drinking score) ///
yline(0) ylabel(#10) xlabel(#20) name(margeffect)


invalid at() dimension information;
using variable male as a factor variable and a regular variable is not
supported
r(322);

end of do-file

Best,

Eddie

[Richard Williams]

You need to make the first occurrence of male also be i.male