Interpreting the intercept in a logistic regression with multiple factor variables

[DB Sobol]

Hi all,

I am looking to calculate the odds ratios in a logistic regression where the dependent variable is a dummy for digital financial service usage. I am using multiple independent variables, including 3 continuous variables, 2 dummy variables, and 2 factor variables. I'm not totally sure how to interpret the constant in the output, as both factor variables have omitted a category. The odds ratio outputs are:

logistic digital income bankacct sendfreq sendtime rec_bankacct i.recepient i.birthplace

digital | Odds Ratio
--------------+------------
income | 3.412442
bankacct| 1.67583
sendfreq| .3388592
sendtime| .3928593
rec_bankacct | 5.432351
_Irecipient_1 | .3849204
_Irecipient_2 | 1.121452
_Irecipient_3 | 1.668443
Ibirthplace_2 | .8439282
Ibirthplace_3 | .6452834
Ibirthplace_4 | 1.152431
_cons| .006926
---------------------------

In this case, would the _cons variable be interpreted as one of the omitted factor variables? And if so, can I still interpret the other variables as is? For example, can the bankacct dummy variable (0=no account, 1=account), be interpreted as: having a bank account increases the odds of using digital financial services by ~68% (OR=1.675) as compared to having no account? Or, would it be ~68% as compared to having no account and (the characteristic of the omitted factor variable).

Hopefully this makes sense, I am happy to clarify if not. Thank you in advance, Statalist!

-DB

[Weiwen Ng]

I am concerned that the output you presented looks like the dummies were generated with the -xi:- prefix (i.e. interaction expansion), but you didn't refer to this in your post. That said, that should make a difference here.

I'm not sure what you mean by

would the _cons variable be interpreted as one of the omitted factor variables?

To be clear, with factor variables, you always omit one category, so the difference in the log odds or odds ratios should always be interpreted as relative to the base category. Then, the constant in the output is the log odds of the outcome with all factor variables at the base category and all continuous variables at 0.

[Richard Williams]

As Weiwen notes, the intercept is the predicted value (in this case, of the log odds) when all other independent variables = 0. That is often an impossible value (e.g. nobody has a score of 0 on a scale that runs from 400 to 1200) so people usually don't pay much attention to it.

Put another way if you have race (1 = white, 0 = nonwhite) and gender (1 = male, 0 = female) in the model the constant would be the expected value for a nonwhite female who had a score of 0 on all the other variables in the model.

[DB Sobol]

Thanks so much to you both!!

Weiwen, I indeed used the -xi- prefix, which appears not to have made it when I pasted the command in the post. Apologies for any confusion that this may have caused!

[Weiwen Ng]

Thanks so much to you both!!

Weiwen, I indeed used the -xi- prefix, which appears not to have made it when I pasted the command in the post. Apologies for any confusion that this may have caused!

No big deal. I intended to say that the -xi- prefix is not needed on almost all estimation commands. Logistic is no exception. You can use the factor variable syntax directly.