Interaction Terms Problem for Logit Regression

[NIki Young]

Hi, I run the following code for logit regression:

logit default i.incomeverified##ib4.income

Income is a category variable with 7 levels. Incomeverified is a dummy. And get result:

| Robust
default | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
1.incomeverified | .599432 .2321633 2.58 0.010 .1444004 1.054464
|
income |
1 | -.8782643 1.085802 -0.81 0.419 -3.006398 1.249869
2 | -.6078613 .3443761 -1.77 0.078 -1.282826 .0671034
3 | -.1656721 .1335863 -1.24 0.215 -.4274963 .0961522
5 | -.3601979 .1678176 -2.15 0.032 -.6891143 -.0312815
6 | .2328037 .1482003 1.57 0.116 -.0576636 .5232709
7 | .2594992 .1557526 1.67 0.096 -.0457703 .5647688
|
incomeverified#income |
1 1 | 0 (empty)
1 2 | 2.787478 .8822793 3.16 0.002 1.058243 4.516714
1 3 | .4686156 .328828 1.43 0.154 -.1758755 1.113107
1 5 | -1.16149 .5804709 -2.00 0.045 -2.299192 -.0237879
1 6 | -1.749303 .5839082 -3.00 0.003 -2.893742 -.6048639
1 7 | -2.237697 .5767056 -3.88 0.000 -3.368019 -1.107375

I want to know how to intepretate the result, the first part is the coefficient of income for incomeverified==0, the second part is the coefficient when incomeverified==1. Am i right?

And when I run marginal effect for this,

margins,dydx(i.incomeverified ib4.income)

incomeverified shows "not estimable". What is the reason for this?
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
1.incomeverified | . (not estimable)
|
income |
1 | . (not estimable)
2 | -.1102621 .0064779 -17.02 0.000 -.1229586 -.0975656
3 | -.028074 .0014621 -19.20 0.000 -.0309395 -.0252084
5 | .0108446 .0018573 5.84 0.000 .0072044 .0144848
6 | .028063 .0023184 12.10 0.000 .0235191 .0326069
7 | .0326274 .0026951 12.11 0.000 .0273452 .0379096

I choose income 4 as the reference group. So does this intepretation correct: verified income level 2 is 11 percentage point less likely to default than income level 4.?

[Ken Chui]

I want to know how to intepretate the result, the first part is the coefficient of income for incomeverified==0, the second part is the coefficient when incomeverified==1. Am i right?

No, the second part is the further adjustment to the first part if incomeverified is 1. For example, when incomeverified is 0 & income = 7, the equation is:

b0 (Where is the constant by the way?) + 0.2594992

Then for incomeverified = 1 & income 7, the interaction also kicks in:

b0 + 0.2594992 - 2.237697

incomeverified shows "not estimable". What is the reason for this?

To get dy/dx you'll need at least two numbers, but for this income category there is only one. It's already a problem in the regression model. Notice that it says "0 (empty)". Generally, there should be a message tugged somewhere in the output, read carefully to find it. It is likely caused by perfect prediction. Aka, all the incomeverified + income group 1 subjects either all have default = 1 or all have default = 0.

[NIki Young]

Thank you Ken. I used income group 4 as a reference group. Could you please tell me what is the economic meaning of 0.2594992 and -2.237697? I understand it represent log odds changes, but the sign of the coefficient can be indicative.
According to your answer, can I say it means when the income is not verified, income group 7 is more likely to default than income group 4. And when income is verified, then income group 7 is less likely to default than income group 4 (since 0.2594992 - 2.237697>0)?