I have data from a conjoint with a "no choice" option. I am not sure, however, how I should model it. From reading the literature, I understand I should add a no-choice constant, but I am not sure how to do this. Any idea? Are you aware of any R tutorial to implement it?
You should add another column in your dataset. Put in 0 for any response that is an actual alternative. 1 for any response that is a "none of the above". Then in your model, you will have an additional coefficient for the "none of the above" option.
Alternatively, you can use Conjoint.ly, which automatically handles these calculations.
[I wanted to comment on K-zar previous comment, but my answer is too long].
"None of the above" is the model intercept (This is why these parameters are called alternative specific constants (ASC)). Let's take an example: You want to model a choice between two options "product" vs "no product" (same as "None of the above"). In this case you could estimate one ASC, let's say for "No product". This means that in your data base, the ASC_No will take the value 1 when option is "No product" and 0 otherwise. Now, we also know that this type of pairwise choice can be re-framed as a binary decision of the differences between the two choice options. Basically we model the proba of the differences to be positive/negative, rather than proba of "No product" utility to be larger/smaller than utility of the other option. The results will be exactly the same. When you will compute the difference terms, you will see that the ASC will correspond to a column of 1's, as the intercept in any other stat model. Perhaps the specificity of multinational logit (MNL) model is to disaggregate the model intercept. If you have more than 2 choice options, then the model intercept will be divided into different components (e.g., effect of 2 vs 1, 3 vs 1, etc).
Sorry I can't comment on k-zar answer (Low reputation). It is important to keep in mind that such alternative-specific constant for the opt-out option ("None of the above") will actually play 2 roles: (1) Capturing the effect of being the opt-out option on observed choices, and (2) simply be a model intercept. Be cautious no over interpreting the meaning of the ASC_None estimate.