Measurement uncertainty in multinomial outcome

Modeling
1

I have a task in which people can answer with non-ordered categories: a, b, c, NA; and can add free text comments.
Reading the comments a non trivial amount say “a bit unsure” or “unsure btw a & b”.

From a conceptual standpoint, I would like to include a measurement error/uncertainty component of the model: e.g. a dirichlet vector with three dimensions (for a, b, and c), where:

  • a (or b, or c) is a v high weight on that dimension
  • “a bit unsure of a” is a high but not v high weight
  • unsure btw a and b distributes most of the weight on a and b (and v little to none to c)
  • NA equally distributes the weight (no preference), or remove, still have to properly think and check on data on this.

There was an early (2018) post on these topics on the forum: Measurement error in a categorical outcome variable, pointing to this paper: Google Scholar

But I was wondering whether there are at least partial implementations of this around as an example?
Suggestions?
Thanks!

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2

Hi Riccardo

A straightforward solution without measurement error might be giving each participant 6 votes and splitting them according to their certainty about the category.

Best,
Bruno

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3

The data is already collected, but I guess an analogous principle could be implemented post-hoc converting answers to votes. A bit more arbitrary (is not sure about a, 4 to a, 1 to b and 1 to c?), but probably better than ignoring the uncertainty. Thanks.

Still if anybody has seen a measurement error model applied to multinomial outcome, I’d be interested in learning from it!

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