Comparing MNL and ML

[Atefeh Fakourrad]

Dear Prof. Michel Bierlaire,

I want to compare the model fits of two models: 1- MNL, 2-ML. I have three questions in this regard:

1- Based on the DCM course, LRS can only be used when the relationship between restricted and unrestricted models is linear, so in this case, LRS cannot be used and we should not look into the models' final log-likelihood, right?

2- Can we use the rho-square/rho-square bar for the initial model? 

2- Reviewing the questions and answers on the forum, I found that you have mentioned that AIC and BIC can also be used in this case. I was wondering if we can easily compare the value of AIC of two models and which one that has a lower value is a better model or like LRS we should consider another table (chi-square)? 

Thanks for your help.

Kind regards,

Ati. 

[Bierlaire Michel]

On 19 Feb 2021, at 10:50, Atefeh Fakourrad <a.fak...@gmail.com> wrote:

Dear Prof. Michel Bierlaire,

I want to compare the model fits of two models: 1- MNL, 2-ML. I have three questions in this regard:

1- Based on the DCM course, LRS can only be used when the relationship between restricted and unrestricted models is linear, so in this case, LRS cannot be used and we should not look into the models' final log-likelihood, right?

Well, it depends on the specification. If you have random parameters in a mixture of logit, the restriction that their coefficients are equal to zero lead to a logit model, and likelihood ratio test can be used.

2- Can we use the rho-square/rho-square bar for the initial model? 

Yes. It is probably better to use AIC and BIC. 

2- Reviewing the questions and answers on the forum, I found that you have mentioned that AIC and BIC can also be used in this case. I was wondering if we can easily compare the value of AIC of two models and which one that has a lower value is a better model or like LRS we should consider another table (chi-square)? 

Yes. See the Wikipedia page for AIC.

Thanks for your help.

Kind regards,

Ati. 

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