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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).

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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.

For sample sizes this large it may be best to not use one of the families of ordinal regression models but rather use multinomial (polytomous) logistic regression. For example, if you used the proportional odds model, some non-proportional odds may result in bias that is not overcome by the lower variance of parameter estimates when compared to multinomial logistic.

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    $\begingroup$ Are there any tricks you can share for modelling this type of response variable with multinomial logistic? Row deletion? Asymmetric loss functions? Guessing you'll recommend to just leave as-is assuming no violations of assumptions. $\endgroup$ – user2763361 Oct 2 '13 at 11:46
  • $\begingroup$ The multinomial logistic model has no assumptions other than linearity and additivity in $X$ (like most other regression models do). $\endgroup$ – Frank Harrell Oct 2 '13 at 12:11

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