goodness of fit

[kiran.t...@gmail.com]

Hi Prof. Bierlaire,

Likelihood ratio test for initial model is one of the outputs provided by teh biogeme for any model. I wanted to ask how can we find the chi-square with this likelihood ratio statistic?

Kind Regards,

Kiran

[Bierlaire Michel]

On 28 Apr 2022, at 06:05, kiran.t...@gmail.com <kiran.t...@gmail.com> wrote:

Hi Prof. Bierlaire,

Likelihood ratio test for initial model is one of the outputs provided by teh biogeme for any model. I wanted to ask how can we find the chi-square with this likelihood ratio statistic?

This test is valid only if the initial model is a restricted version of the model, that has been estimated with maximum likelihood. 

Typically, it happens when you estimate a logit model, and you use the estimated values to estimate a nested logit model.

It is then a classical likelihood ratio test, distributed as a chi square where the number of degrees of freedom is the difference between the number of parameters of the two models. 

Note that Biogeme includes a tool for likelihood ratio test, documented here:

http://biogeme.epfl.ch/sphinx/tools.html#biogeme.tools.likelihood_ratio_test

It calculates also the value of the chi2. 

Kind Regards,

Kiran

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