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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 logistic 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)

I want to understand the coefficients of the dummies.
If Dummy16 is equal to +20, does it mean that the event is more likely to happen in 2016? Is it a percentage?
I don't understand the fact that it can be equal to a high number, since both the dependent variable and the dummies can only be equal to 0 and 1.

Side note: I don't know if it is relevant, but I invented the coefficient of Dummy16, and, maybe, in this simplified case it can't be equal to +20. So, for the sake of clarity, I will specify that, in my actual database, I have 9 dummies for the years from 2013 to 2021 and the actual coefficients are:
Dummy13 = +13
Dummy14 = +23
Dummy15 = +13
Dummy16 = +6
Dummy17 = +0.6
Dummy18 = -25.4
Dummy19 = -51
Dummy20 = -65.8
Dummy21 = -23

Andrea Brama
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  • You sound like in a decision between a multinomial and a binary logistic regression, right? Then maybe this and similar threads are helpful. – ttnphns Sep 24 '22 at 12:41
  • No, I just would like to understand how to interpret the coefficients, I am not in a decision between multinomial and binary logistic regression. What do the coefficients of the dummy mean? – Andrea Brama Sep 24 '22 at 13:51
  • How to interpret coefficients of dummy predictors? This topic has been covered million of time. One general introduction of contrast variables such as dummy and other types is here, for example. – ttnphns Sep 24 '22 at 14:10
  • Ok but dummy variables in a logit regression. I know that, for example, if I have a regression where the dependent variable is the death rate, and I have dummies indicating the US states, the coefficient of the dummies will indicate how the death rate varies with respect to the state taken as base level. I do not understand however how it works on the logit regression, and how the coefficient can be higher than 1 – Andrea Brama Sep 24 '22 at 14:37
  • Logistic regression is a linear regression via logit link function. Whereas in linear regr. we interpret b (a regr. coef), in logistic regr. we interpret exp(b). – ttnphns Sep 24 '22 at 15:18
  • Please do not reask the Q, but edit the original version! – kjetil b halvorsen Sep 26 '22 at 00:26

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