# Rare event ordinal logit with discrete response $Y_t \in \{1,2,3\}$

I have a response variable in $Y(t) \in \{1,2,3\}$ and I am considering to use ordinal logit to model it. We have $3000$ instances of $Y(t)=1$, $3000$ instances of $Y(t)=3$ and $2\,000\,000$ instances of $Y(t)=2$. Is the ordinal logit appropriate here or is there a better choice (Poisson, negative binomial, multinomial logit etc)? Note that my main focus is on modelling $Y(t)=1$ and $Y(t)=3$ accurately. If I misclassify $Y(t)=2$ out of sample then the consequences aren't as bad. Some sort of asymmetric loss function may be appropriate.

Also note that this is a time-series prediction problem, and $Y(t)$ doesn't display severe autocorrelation, but $Var(Y)$ is time-varying (as in you will get long stretches of $Y(t) = 2$ only then a stretch of time where it's more variable).

As a side note, thinking of this as a classification problem rather than a problem of predicting the probability that $Y=y$ will likely run into trouble.
• The multinomial logistic model has no assumptions other than linearity and additivity in $X$ (like most other regression models do). – Frank Harrell Oct 2 '13 at 12:11