I'm currently and frequently using outcomes that are Likert items or summated scales from Likert items, and they exhibit reverse-J-shaped or J-shaped distributions. The distributions stack up (say) at the lowest scale point, much like a count variable for a bad outcome would, but the variables are ratings, not counts.
I'd appreciate some recommendations about how you think such outcomes could/should best be modeled in Mplus? I've used Poisson/negative binomial regression, but the interpretation is awkward because the variable is not really a count.
In some cases, when there is actually a two-tailed distribution following the lower bound (say, zero) a two-part model works well. But in other cases, the response is just an ordinal Likert item (say, 0-10) and the distribution of the ratings descends to the right from zero; or if it's a good thing, descends from the left from 10.
What little I know about censored (Tobit) regression makes that seem like an incorrect approach. But so does Poisson/negative binomial regression.