Multinomial Logit when you may not observe outcome accurately

[George Ford]

Say your job is to collect data by determining whether bugs A, B, or C are observed in a given area. The bugs are tiny, and you may or may not observe their presence since you doing it by a visual survey. Ignoring the observation issue, you'd use MNL to determine what factors influence presence (none, one, two, or three presences). But, this wouldn't account for the fact there would need to be enough of them to observe or else you're hungover and just missed it.

I was thinking some type of inflated MNL model would work.

Any ideas?

Does Stata have an inflated MNL program?

Thanks for any help provided.