# Hybrid choice model and log-likelihood

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### Saha

May 5, 2020, 3:13:50 AM5/5/20
to Biogeme
Hello,

I have estimated a latent choice model with five latent variables to compare it with a multinomial choice model with python biogeme. However, the absolute amount of log-likelihood of the hybrid model is significantly higher than MNL (Final log-likelihood for HCM: - 431565 and  MNL:-5623.32) with HCM adusted rho-squared: 0.005 and MNL adjusted rho-squared: 0.23.

Is that normal? Should I calculate log-likelihood and adjusted rho-squared for HCM with a different method if I want to compare it with MNL? If yes, it will be much appreciated to have your suggestion?

Kind regards,

### Michel Bierlaire

May 5, 2020, 3:26:38 AM5/5/20
to sahba.g...@gmail.com, Michel Bierlaire, Biogeme

On 5 May 2020, at 07:21, Saha <sahba.g...@gmail.com> wrote:

Hello,

I have estimated a latent choice model with five latent variables to compare it with a multinomial choice model with python biogeme. However, the absolute amount of log-likelihood of the hybrid model is significantly higher than MNL (Final log-likelihood for HCM: - 431565 and  MNL:-5623.32) with HCM adusted rho-squared: 0.005 and MNL adjusted rho-squared: 0.23.

Is that normal?

Of course. The likelihood of the HCM combines the choice model as well as the measurement equations of the indicators.

Should I calculate log-likelihood and adjusted rho-squared for HCM with a different method if I want to compare it with MNL? If yes, it will be much appreciated to have your suggestion?

You can calculate the likelihood of the choice model only for the HCM. But keep in mind that it is not the maximum likelihood, and classical tests cannot be applied.
Goodness of fit is not the only thing that matters in a model. You need to check which model is achieving your goals. If you want to predict market shares, perform a out-of-sample validation.

Kind regards,

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Oct 4, 2021, 3:55:14 PMOct 4
to Biogeme
Dear Prof. Michel Bierlaire,

I have estimated a simultaneous HCM using PandasBioegem. The thing is that the final loglikelihood is much worse (-28866) than the null loglikelihood (-2395). Does this mean that the null model (random choice) performs much better than HCM?

There is also an initial loglikelihood in the output which is -4412. What does the initial loglikelihood imply?

As the last question, what is the difference between Rho-squared and adjusted Rho-squared?

Kind regards,
Ati.

### Bierlaire Michel

Oct 4, 2021, 4:14:15 PMOct 4
to a.fak...@gmail.com, Bierlaire Michel, Biogeme

On 4 Oct 2021, at 16:31, Atefeh Fakourrad <a.fak...@gmail.com> wrote:

Dear Prof. Michel Bierlaire,

I have estimated a simultaneous HCM using PandasBioegem. The thing is that the final loglikelihood is much worse (-28866) than the null loglikelihood (-2395). Does this mean that the null model (random choice) performs much better than HCM?

It does not mean anything. The null loglikelihood is for the choice model only. These two values cannot be compared.

There is also an initial loglikelihood in the output which is -4412. What does the initial loglikelihood imply?

It is the log likelihood calculated with the initial values of the parameters.

As the last question, what is the difference between Rho-squared and adjusted Rho-squared

It seems that you have not read the documentation…
It is also explained in the Ben-Akiva and Lerman book.

Kind regards,
Ati.

On Tuesday, May 5, 2020 at 9:26:38 AM UTC+2 michel.b...@epfl.ch wrote:

On 5 May 2020, at 07:21, Saha <sahba.g...@gmail.com> wrote:

Hello,

I have estimated a latent choice model with five latent variables to compare it with a multinomial choice model with python biogeme. However, the absolute amount of log-likelihood of the hybrid model is significantly higher than MNL (Final log-likelihood for HCM: - 431565 and  MNL:-5623.32) with HCM adusted rho-squared: 0.005 and MNL adjusted rho-squared: 0.23.

Is that normal?

Of course. The likelihood of the HCM combines the choice model as well as the measurement equations of the indicators.

Should I calculate log-likelihood and adjusted rho-squared for HCM with a different method if I want to compare it with MNL? If yes, it will be much appreciated to have your suggestion?

You can calculate the likelihood of the choice model only for the HCM. But keep in mind that it is not the maximum likelihood, and classical tests cannot be applied.
Goodness of fit is not the only thing that matters in a model. You need to check which model is achieving your goals. If you want to predict market shares, perform a out-of-sample validation.

Kind regards,

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Oct 5, 2021, 4:23:10 PMOct 5
to Biogeme
Thanks, Prof. Bierlaire for the reply. I have estimated an HCM model. As instructed, we defined two parameters (Delta1 and Delta2) to include the Likert scale with 5 levels. I was wondering what the interpretations of these parameters are?

As an aside, just curious to know if it is possible to include the latent variables with only the measurement model (just indicators), not the structural model?

Best,
Ati.

### Bierlaire Michel

Oct 6, 2021, 5:01:55 AMOct 6
to a.fak...@gmail.com, Bierlaire Michel, Biogeme

On 5 Oct 2021, at 13:36, Atefeh Fakourrad <a.fak...@gmail.com> wrote:

Thanks, Prof. Bierlaire for the reply. I have estimated an HCM model. As instructed, we defined two parameters (Delta1 and Delta2) to include the Likert scale with 5 levels. I was wondering what the interpretations of these parameters are?

The Likert scale is a discrete output. The measurement equations provide a (latent) continuous output. The thresholds defined by the delta’s are mapping the latent continuous values and the discrete levels.

As an aside, just curious to know if it is possible to include the latent variables with only the measurement model (just indicators), not the structural model?

Well, the structural equations define the latent variable. Indeed, by definition of “latent”, it is not observed. It cannot therefore be used as a measurement.