Hi Mollalign,

Let me begin with that you need dis-aggregate observations (individual choices, not only aggregate count of choices) to be able to construct a multinomial choice model.

But your question may be what if, for example, 999 out of 1000 individuals choose alternative A over B. The answer is that the multinomial model might become under-identified and might not be solved.

I am not sure if there is an absolute percentage as the minimum choice count requirement. I have estimated (calibrated) models with choices less than 1 percent, and I have been stuck with choices more than ten percent. Because choices, attributes and variables make a complex system in a model, you have to try it to see if it works or not.

Having said that, I think in case of unlabelled choice experiments -where you want to design a survey and your alternatives do not have labels- you can play with your attributes to avoid such identification problems.

Amir Pooyan Afghari ,thank you for your response.

you have mentioned a good point on checking how the model works or not due to variability of choices, attributes and variables . But I have a question for you in case of revealed preference survey.

--> In what way you checked the percent you have is enough for modeling? (you used less than 1 percent and also more than 10 %....could you tell me more on the challenge you got in your model calibration?)

-->what is your criterion for checking the model works or not?

I'm not sure if I understand your question Mollalign. What do you mean by "enough for modelling"? Do you mean how I ensured that the sample is a proper representation of my population? Well, I estimated my model on several random samples from the data to ensure model parameters are not biased.

Please note that people's choice behaviour is not something you can play with. You cannot choose to use or discard the data based on a certain threshold (e.g. percentage) because this would create self-selection biases. If the data tells you that the percentage of people choosing bus, for example, is 1 percent, then you cannot manipulate it to be higher.

The challenge I was confronted with was model identification meaning that the hessian matrix of the model parameters gets very close to zero and so standard errors become infinity. In fact, there are either infinite combinations or no combination at all, that can result in model parameters. But, again, this is merely a property of the data i.e. there is not enough variation in choices versus attributes. Usually this must not happen given that you have randomly selected your individuals and the sample size is more than 50 (only as a rule of thumb, not as an absolute criterion).

After all, I would add that a good model will have:

1- convergence of the maximization algorithm

2- intuitive parameter estimates

3- valid standard errors

3- proper t-values (extremely large t-values, like 500 or more) are a sign of model mis-specification)

but again, even a model that has all o the above may not be a perfect model. It is your judgment that your model is perfectly correct or not.