I estimated a model for which I tested the assumption that the effect of my variable of interest is homogeneous for observations belonging to two different groups (for simplicity assume rural/urban).
Results show that, on the one hand, both the main effects are not statistically different from zero*, on the other the interaction term is statistically significant. This denotes a cross-over interaction where the effect changes direction in sign according to the group being considered.
In this particular example I constructed the dummy as 1 if the observation is a rural household, 0 otherwise. As anticipated above the only statistical significant coefficient is that of the interaction term, which is negative (-0.62), thus the overall effect for rural households coincides with the interaction's coefficient.
I thus reject the assumption that the effect of my variable of interest is homogeneous for the two groups. However, I am interested to see the extent of this switch in sign of the coefficient of interest.
Conversely, if I construct the dummy in the opposite way (i.e 1 if the observation is urban, 0 otherwise) and estimate the same model. I get the following results:
- interaction: statistically different from zero (0.62);
- main effect of variable of interest: statistically different from zero (-0.63);
- main effect of the dummy defining the groups: not statistically different from zero.
The overall effect of the interest variable for urban households equals -0.01.
However, two questions arise:
- Given the detection of a cross-over interaction in the first specification, is it worth computing and showing the results re-computing the dummy for rural/urban as in specification two above? As a reader I would like to see at what extent the effect is positive (something I cannot see from the results of specification one).
- Can I still talk of cross-over interaction even if in specification two I get a rather very small but still negative and significant effect?
Note: Statistical significant results are those for which p<0.05; for not statistically significant results p>0.1.