Confusing Interaction Terms

[Ryan Clukey]

Hello Forum,

I'm working on a panel model using negative binomial regression. I have an independent variable (binary) and a moderating variable (logged) that were found to have a significant interaction. I could use some assistance in determining what is going on. The coefficient of each term individually is negative, but the interaction term is positive. Additionally, when I produce the margins plot, the slopes for each categorical group slope down. However, if i simply plot (scatter plot) the original data (the moderator variable against the DV), the "trend" of the data slopes up. How can this be?


In the example provided, the scatter plot show the original, un-modeled data, covariate against the DV. I ran the model (XTNBREG), and it found the IV to be significant (negative coefficient) and the moderator to be significant (negative coefficient), and the interaction between them to also be significant (positive coefficient). When STATA plotted the margins, it shows the interaction lines sloping down - it seems to contradict the original scatter plot.

It might also be helpful to know that the DV is skewed with a lot of zeros. However, the variance is greater than the mean - hence NBREG.

Any assistance is appreciated.

[Clyde Schechter]

If you had read the Forum FAQ carefully, you would have learned that using Microsoft Word attachments to show results is not helpful. Some of the most frequent responders here do not use Office. And others, like myself, who do, will not download a Word document from a stranger because they can contain active malware. It's too risky. So you have, in effect, shown only a part of your results, the scatterplot. Nothing can be said without more information in a fully usable format. This entails reading FAQ #12 carefully and following the advice given there.

[Ryan Clukey]

Hello Clyde, yes, I saw that, but I'm having difficulty learning STATA and importing the code / results here in a format that can still be read. While I work on that, here's a screen shot of the model results / margins... not in a word document.

[Clyde Schechter]

Well, I see why you find this confusing. What you have, in the scatter plot, is an optical illusion. The appearance of a positive relationship between log income and your count income is conveyed by the large territory dotted by points heading up as high as 800. But notice how sparse those points are. There is hardly any overlap among them, and plenty of empty space between them. Although they stand out to the eye, the represent a tiny fraction of the data.

Now fix your gaze on the bottom of the scatterplot. Notice the dense dark blob near the horizontal axis. This dense dark blob is the result of a huge number of data points overlapping each other. These points are the bulk of the data. And although its contour appears to rise a bit between 0 and 4 on the horizontal axis, after that it falls off. This is the signal in your data. The big sparse mass of points up higher is just the noise. Indeed, given that the negative binomial model accommodates overdispersion, it is entirely credible to have noise values up to 800 with an expected value embracing zero.

The margins plots in the second graph are a faithful reflection of the negative binomial results. The coefficient of log income for females is -0.288, and that for males is -0.288 + 0.252 which is -0.036, small but still negative. Your female line descends unambiguously, and the male line is much less steep, almost flat. That's exactly what the model says. And the model looks to me as if it does reflect the data well.

[Ryan Clukey]

you are a genius. Thank you kindly!

[Ryan Clukey]

That explains why the IRR is 1.28, because it is the relative difference from female to male. In other words, for every 1-unit change in log(income), males hold 28% more jobs than females...

[Clyde Schechter]

Yes, that's right, assuming that your DV is a count of jobs.