# how to interpret significance of exp(beta) in size function of destination choice model

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### Mariska

Oct 19, 2021, 8:18:08 AMOct 19
to Biogeme
Dear Michel Bierlaire,

I am estimating a destination choice model with size function (in order to include destination attractiveness based on # inhabitants, # jobs and # student spots). Hence, my utility function has the following form (based on the NRM documentation, see attached):

U = b1x1 + b2x2 + log(b3x3 + exp(b4)*x4)

Now, how should I interpret the significance of b4? Should I still consider the difference from zero (e.g. at 5% significance level (P<0.05)) as provided in biogeme results or does that not hold any longer, since it is added as an exp within a log?

I have added the biogeme part of my code for clearity on the utility function.

I hope you can shed some light on this matter. Thank you very much!

Greetings, Mariska
Biogeme part of code.py
size function.png

### Bierlaire Michel

Oct 19, 2021, 11:15:37 AMOct 19
to m.van.e...@gmail.com, Bierlaire Michel, Biogeme

On 15 Oct 2021, at 17:25, Mariska <m.van.e...@gmail.com> wrote:

Dear Michel Bierlaire,

I am estimating a destination choice model with size function (in order to include destination attractiveness based on # inhabitants, # jobs and # student spots). Hence, my utility function has the following form (based on the NRM documentation, see attached):

U = b1x1 + b2x2 + log(b3x3 + exp(b4)*x4)

Now, how should I interpret the significance of b4? Should I still consider the difference from zero (e.g. at 5% significance level (P<0.05)) as provided in biogeme results or does that not hold any longer, since it is added as an exp within a log?

By significance, you mean the t-test, I guess. The reported t-test tests the hypothesis that the parameter is equal to zero, which is of no interest to you in this case.

I have added the biogeme part of my code for clearity on the utility function.

I hope you can shed some light on this matter. Thank you very much!

Greetings, Mariska

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<Biogeme part of code.py><size function.png>

### Mariska

Oct 20, 2021, 2:56:01 AMOct 20
to Biogeme
Dear Michel,

Thank you for your reply. Indeed, I meant the t-test (I am sorry for not being clear).

So, I understand now that the t-test with hypothesis that the parameter is equal to zero, is not of interest in this case. However, what hypothesis should I test instead?

Kind regards,
Mariska

### Bierlaire Michel

Oct 21, 2021, 7:33:44 AMOct 21
to m.van.e...@gmail.com, Bierlaire Michel, Biogeme

On 20 Oct 2021, at 10:43, Mariska <m.van.e...@gmail.com> wrote:

Dear Michel,

Thank you for your reply. Indeed, I meant the t-test (I am sorry for not being clear).

So, I understand now that the t-test with hypothesis that the parameter is equal to zero, is not of interest in this case.

Exactly.

However, what hypothesis should I test instead?

Well, this is your model. You should know the modeling hypotheses that you want to challenge.

Kind regards,
Mariska

On Tuesday, 19 October 2021 at 17:15:37 UTC+2 michel.b...@epfl.ch wrote:

On 15 Oct 2021, at 17:25, Mariska <m.van.e...@gmail.com> wrote:

Dear Michel Bierlaire,

I am estimating a destination choice model with size function (in order to include destination attractiveness based on # inhabitants, # jobs and # student spots). Hence, my utility function has the following form (based on the NRM documentation, see attached):

U = b1x1 + b2x2 + log(b3x3 + exp(b4)*x4)

Now, how should I interpret the significance of b4? Should I still consider the difference from zero (e.g. at 5% significance level (P<0.05)) as provided in biogeme results or does that not hold any longer, since it is added as an exp within a log?

By significance, you mean the t-test, I guess. The reported t-test tests the hypothesis that the parameter is equal to zero, which is of no interest to you in this case.

I have added the biogeme part of my code for clearity on the utility function.

I hope you can shed some light on this matter. Thank you very much!

Greetings, Mariska

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