How would we model cumulative voting ($100 method) in brms
?
For example:
Q1: What food do you like out of these five alternatives? A,…,E
Q2: What do you like to drink out of these four alternatives? A,…,D
Each respondent can pick many different strategies, e.g., one could put all $100 on category no. 1 in Q1, while another might spread them out $20 each on each category.
{100, 0, 0, 0, 0}
{20, 20, 20, 20, 20}
In Q2 they have $100 again to spend, and there some might choose to spend $25 on each category, while some might put $80 on category 2 and $20 on category 3.
{25,25,25,25}
{0,80, 20, 0}
In short, in each category, they can place 0-100. The total must be 100 for each question.
I was first thinking a categorical ordered outcome, but is it really that? Compared to a Likert scale, one can pick many categories. In addition, to me, it’s a bit different if two people answer the following on Q1:
{0,10, 20, 30, 50, 0}
{0, 5, 10, 10, 65, 0}
My friend and I discussed this today and he mentioned Dirichlet, and that sounds plausible.