# Why is my interaction term significantly negative when its constituents are both significantly positive?

So I'm conducting a logistic regression model with 'voted_trump'(1=voted for trump, 0=didn't vote for trump) as my dependent variable. My hypothesis is that opposition to political correctness ('OPC', a 1-4 ordinal scale) predicts a greater likeliness of having voted for Trump, net of all controls. This expected relationship remains significant until I add an index of conservative talk-radio consumption (where 0=no consumption, 5=listens to 5 conservative radio programs) to the model. In case it's relevant, I should note that its inclusion also trimmed the number of observations from 2400->1400. The unique effect of conservative radio on voting for Trump, however, was also insignificant. I thus constructed and tested an OPCxCR interaction term to determine their joint effects. In the end, both constituent terms became significantly positive while the OPCxCR interaction was significantly negative. Not sure how to interpret this, so would appreciate some input. Thanks in advance! This means that higher levels of OPC and CR are predictive of voting for Trump, but that the effect of OPC on voting for Trump diminishes as the level of CR increases and that the effect of CR on voting for Trump diminishes as the level of OPC goes up.

More than that can't be said unless you give the actual coefficients.

One way to visualize this is to make a table with 20 rows - one for each combination of OPC and CR - and the probability of voting for Trump. You can also graph this.

As an aside, note that you are treating OPC and CR as if they were continuous variables. This is not necessarily wrong, but you should be aware of it.

EDIT The OP added the coefficients. So, the three key ones for this question are OPC (range 0-4), CR (0-5) and the interaction. These are 0.28, 1.85 and -0.50.

When OPC is 0, the effect of each one point increase in CR is to multiply the likelihood of voting Trump by $e^{1.85}=6.36$. But when OPC is 5, the effect of each one point increase in CR is $e^{1.85 + 5*(-0.5)} = e^{-0.65} = 0.52$.

Others combinations can be calculated similarly.

This seems intuitively like a poor model. Perhaps my point about linearity is serious. You might look into optimal scaling.

• Hey Peter, I've added the results to the above to make things clearer. Thanks for helping me out! – Zach Goldberg Jul 28 '17 at 22:19
• Peter, Thanks again for following up! "the effect of each one point increase in CR is to multiply the likelihood of voting Trump by e1.85=6.36e How did you obtain that figure? (i.e., what did you multiply 1.85 by to get 6.36). "This seems intuitively like a poor model. Perhaps my point about linearity is serious. You might look into optimal scaling." It's certainly not the most parsimonious. I was simply interested in determining whether OPC was a campaign factor in its own right or whether it could be largely explained by other measures of prejudice/political attitudes. – Zach Goldberg Jul 31 '17 at 18:47
• "You might look into optimal scaling" I'm interested, but care to elaborate? – Zach Goldberg Jul 31 '17 at 18:51
• Optimal scaling is a method of assigning the best values to ordinal and nominal data for the regression to "work". It's available in R in the homals package and the opscale package, and in SAS in PROC TRANSREG. – Peter Flom Jul 31 '17 at 22:01
• Thanks Peter. Any idea if there is there a comparable package for stata 14? – Zach Goldberg Jul 31 '17 at 22:03