Minimum number of choice tasks

[pakhi]

Hi team,

I am designing a DCE with 3 alternatives (follow-up A, follow-up B, and None). In my study, ‘none’ indicates that respondents do not prefer any of the provided options (A and B), but it does not necessarily mean that they do not prefer other available follow-up at all.

I used the below formula to estimate minimum number of choice tasks:
S_min = L/(A-1)
Where S_min is the minimum number of choice tasks, L is the total number of levels of all attributes, and A is the number of alternatives.

Should the above formula include ‘none’ option in the alternatives? In other words, should it be A=2 or A=3? I am uncertain whether selecting ‘none’ contributes any information on trade-offs that respondents are willing to make among attribute levels.

Thank you.

Kind regards,
Pakhi

[Michiel Bliemer]

The minimum number of choice tasks is K/(A-1), where K is the number of parameters to estimate, including any constants and coefficients of dummy variables, and where A is the number of alternatives, including the opt-out (none) alternative (so A=3 in your case). For each categorical variable with L levels, the number of parameters is L-1.

Note that this is a theoretical minimum, you probably want more than that. I generally recommend multiplying this minimum number of choice tasks with at least 3 to ensure that there is sufficient variation in the data to estimate models.

Michiel