How do I interpret different results in a standard and a mixed logit model?

[Tarapada Mandal]

Dear professor Bierlaire,

I have calibrated a standard and a mixed logit model (with different combination of distribution of betas) and I have estimated three parameters (as I am testing three factors) in a stated choice experiment. I have found all three parameters significant and negatively affecting the choices (negative signs for all the parameters) in standard logit model. But while calibrating different mixed logit model, I have found different result. Taking log-normal distribution for one parameter and normal distribution for the other two parameters improves the log-likelihood and the adjusted rho squared value. But taking log-normal distribution of one parameter changes the sign of the parameter though the model fitting improves. How do I interpret the results? Should I consider the parameter to be positive as taking a log normal distribution gives best fit in mixed logit model in terms of loglikehood and adjusted rho squared? or I should take it negative as in case of standard logit model (where adjusted rho squared values are less) Any suggestions please?

Regards.

[Michel Bierlaire]

On 3 May 2019, at 07:40, Tarapada Mandal <tarapadam...@gmail.com> wrote:

Dear professor Bierlaire,

I have calibrated a standard and a mixed logit model (with different combination of distribution of betas) and I have estimated three parameters (as I am testing three factors) in a stated choice experiment. I have found all three parameters significant and negatively affecting the choices (negative signs for all the parameters) in standard logit model. But while calibrating different mixed logit model, I have found different result.

It happens when the number of draws is insufficient.

Taking log-normal distribution for one parameter and normal distribution for the other two parameters improves the log-likelihood and the adjusted rho squared value.

It is always the case.

But taking log-normal distribution of one parameter changes the sign of the parameter though the model fitting improves.

As lognormal has positive support, you decide about the sign. And you should choose the sign that corresponds to the behavioral interpretation. 

 

How do I interpret the results? Should I consider the parameter to be positive as taking a log normal distribution gives best fit in mixed logit model in terms of loglikehood and adjusted rho squared? or I should take it negative as in case of standard logit model (where adjusted rho squared values are less) Any suggestions please?

Regards.

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