I am using a fixed effects multinomial logit model (femlogit) with interaction terms. There are three possible outcomes, with outcome(1) being the baseline/default. I have an interaction between two continuous variables, and I am unsure how to interpret the odds ratios, especially since the odds ratios associated with the interacted variables' main effects really jump around. I understand that being a ratio means such fluctuations are possible, but I am:
1) concerned that the fluctuations somehow mean something is "wrong", and
2) unsure how to make sense of the two main effects plus the interaction.
Code:
femlogit f.y x1-x10 x1*x2, robust or
A few things: femlogit doesn't allow operators like "#", so interaction terms need to be calculated by hand (hence "x1*x2" as the interaction here). Next, x1 is log transformed.
I'm not reproducing the entire output, but here's what the odds ratios of interest look like in the case of outcome 3 (relative to outcome 1):
| x1 |
1.04* |
1.04* |
|
-1.99 |
-2.04 |
| x2 |
0.24 |
1.04e+06* |
|
(-0.70) |
-2.34 |
| x3 |
11.52 |
7.53 |
|
-0.82 |
-0.67 |
| x4 |
0.42* |
0.44* |
|
(-2.56) |
(-2.45) |
| x5 |
0.94 |
0.98 |
|
(-0.29) |
(-0.10) |
| x6 |
0.92 |
0.92 |
|
(-0.93) |
(-0.93) |
| x7 |
0.92 |
1.02 |
|
(-0.01) |
0 |
| x8 |
0.02 |
0.03 |
|
(-1.25) |
(-1.15) |
| x9 |
1 |
0.99 |
|
(-0.06) |
(-0.10) |
| x10 |
1.72** |
1.74** |
|
-10.48 |
-10.6 |
| x1*x2 |
|
0.16** |
|
|
(-2.80) |
As said, the odds ratio for x2 has me concerned. As for the interaction term, I read a post by Maarten Buis
in a related thread in which he said the way to interpret the interaction effect is to calculate it across a meaningful range of x1 or x2 (I guess either). If I were interested in -1SD to +1 SD for x1, that range would be 5 (like I said, this is a log-transformed currency based value). That would mean like
di (exp(_b[c.x1#c.x2]*5)-1)*100 = 25%. That is certainly interesting, if true. But what about the ORs for x1 and x2 in isolation? Are they not to be included in this calculation somehow?
Sorry if this is really basic. If anyone has a simple formula for how to explain the relationships of interest in a straightforward yet meaningful way, I'm all ears.