The difference between 'logit' function and 'loglogit' function in models module

[Zheren Liu]

Dear all, 

I have a question about the 'logit' function and the 'loglogit' function in the 'models' module of Biogeme. In  A short introduction to PandasBiogeme, the demo implement the choice model by models.loglogit. And I just tried the models.logit with the same swissmetro data. And found the results are different. 

This is the results estimated by the logit model:

And this is the results estimated by the loglogit model:

I checked the source code, and found that the only difference between 'logit' function and the 'loglogit' function is that  'loglogit ' returns the logarithm of the probability while the 'logit' return the original probability. I'm a little confused. In my view, although the expression of probability in these two models are different,  the estimated parameters should be the same, since the logarithm will not change the extreme point. However, actually the results are different. And I don‘t know why. 

I'd appreciate it if you could help. 

Best regards, 

Zheren Liu

Sept. 13th, 2021

[Bierlaire Michel]

Biogeme requires the definition of the log of the likelihood function.
For logit, you can do it in two ways:

logprob = models.loglogit(V, av, CHOICE)

or

from biogeme.expressions import log
logprob = log(models.logit(V, av, CHOICE))

Both are entirely equivalent and provide the same results.

The former is more efficient from an implementation point of view. This is why it is made available.

> On 13 Sep 2021, at 14:20, Zheren Liu <zrli...@gmail.com> wrote:
>
> Dear all,
>
> I have a question about the 'logit' function and the 'loglogit' function in the 'models' module of Biogeme. In A short introduction to PandasBiogeme, the demo implement the choice model by models.loglogit. And I just tried the models.logit with the same swissmetro data. And found the results are different.
>
> This is the results estimated by the logit model:

> <屏幕截图 2021-09-13 201605.png>
> And this is the results estimated by the loglogit model:

> <屏幕截图 2021-09-13 201605.png>
>
> I checked the source code, and found that the only difference between 'logit' function and the 'loglogit' function is that 'loglogit ' returns the logarithm of the probability while the 'logit' return the original probability. I'm a little confused. In my view, although the expression of probability in these two models are different, the estimated parameters should be the same, since the logarithm will not change the extreme point. However, actually the results are different. And I don‘t know why.
>
> I'd appreciate it if you could help.
>

> <屏幕截图 2021-09-13 201611.png>

> <屏幕截图 2021-09-13 201611.png>
>
> Best regards,
> Zheren Liu
> Sept. 13th, 2021
>

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> <屏幕截图 2021-09-13 201605.png><屏幕截图 2021-09-13 201611.png><屏幕截图 2021-09-13 201611.png><屏幕截图 2021-09-13 201605.png>