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I wanted to know what is the difference between running a multinomial logit regression and a logit regression on a model in which the dependent variable is a dummy with just two levels.

My database looks like this

Firm     Event      Year       Info       Dummy14      Dummy15     Dummy16
1        0          2014        x           1             0           0
1        0          2015        x           0             1           0
1        1          2016        x           0             0           1
2        0          2014        x           1             0           0
2        1          2015        x           0             1           0
3        0          2014        x           1             0           0
3        0          2015        x           0             1           0
3        0          2016        x           0             0           1
4        1          2014        x           1             0           0

Basically, I have analysed some firms for the years 2014-2016, eliminating them if an event happens. I have also added some dummies (equal to 1 if we are in a specific year) to implement a year fixed effects model.

The regression is the following:

Event ~ Info + Dummy14 + Dummy15 + Dummy16

(I want to check if the info in the year previous to the event are different from the other years)

If I use

Analysis = glm(Event ~ Info + Dummy14 + Dummy15 + Dummy16,  
     data=Database, family="binomial")

I have the following warning:
glm.fit: the algorithm did not converge
glm.fit: fitted probabilities numerically 0 or 1 occurred

While if I use

Analysis = multinom(Event ~ Info + Dummy14 + Dummy15 + Dummy16, 
     data=Database)

Everything seems to run perfectly.

How is this possible?

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    $\begingroup$ To start with they use different cost functions in optimization. In your case multinomial logit is the same as a simple binary logit, of course. What glm is complaining for is that your dummies perfectly explain your training sample and there’s no uncertainty left $\endgroup$
    – Aksakal
    Sep 23 at 17:01
  • $\begingroup$ Ok perfect, and another question: how do I interpret, for example, the fact that the coefficient of Dummy16 is +30? Is it an error? Both Event and Dummy16 can only be 0 or 1... $\endgroup$ Sep 23 at 17:20
  • $\begingroup$ Show the full output of both models, that can help understand the issue. Also consider how many combinations are possible of dummies. If you have 3 dummies then it’s only 8. $\endgroup$
    – Aksakal
    Sep 23 at 17:46
  • $\begingroup$ In reality, the number of year dummies is 9 (from 2013 to 2021) but, sticking to the simpler model I presented above, how do I comment a coefficient of +6 for dummy16 for example? $\endgroup$ Sep 24 at 7:37
  • $\begingroup$ Does it mean that the event is more likely to happen in 2016? Or is it a percentage? $\endgroup$ Sep 24 at 8:44

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