Context: I'm testing a hypothesis for a paper I have to write. I suspect that higher trait authoritarianism (sca) will positively predict greater support for US Supreme Court Justice Roberts (data gathered post affordable care act ruling) on its own, but will increase the negative effects of conspiratorial ideation (CI) in an sca x CI interaction. I tested the interaction in the model below and it was significantly negative. I'm not sure though whether the results suggest that sca buffers/offsets the negative effects of CI or intensifies them. Can someone take a look and explain to me how to interpret it?
$\begingroup$ It means that the higher CI is, the relationship between sca and the outcome is getting more negative. Or formulated differently: the relationship between CI and the outcome is getting more negative the higher sca is. Specifically, the slope of CI is positive for values of sca $< -3.01$ and negative for sca $> -3.01$. Similarly, the slope of sca is positive for CI $< 1.90$ and negative for CI $> 1.90$. $\endgroup$– COOLSerdashDec 3, 2017 at 11:10
$\begingroup$ Here is a good tutorial on how to visualize the interaction in Stata. $\endgroup$– COOLSerdashDec 3, 2017 at 14:47
$\begingroup$ As my old stats teacher always told us: when in doubt calculate the derivative $\endgroup$– RepmatDec 3, 2017 at 15:52
At the moment, you cannot tell by examining the interaction. All that you currently know is that SCA positively predicts support for Roberts with C.I and the interaction in the model, and that C.Ideation negatively predicts support for Roberts with SCA and the interaction in the model. These to effects are, however, qualified, by the higher order SCA x CI interaction (-.6398, t = -4.15,p < .001). So, you know that they interact, but you do not know what that interaction looks like. You would need to decompose this interaction into its two simple slopes to examine if either is significant. Use Aiken & West, 1991 as a conceptual guide, and then use some of the online excel calculators (e.g., Jeremy Dawson has an easy one) to plot the simple slopes.