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Suppose we are interested in an outcome variable $Y$. It can take four values $1,2,3,4$. These are categories. What would a probit link function do as opposed to a proportional odds model? Would a probit link model the outcome as $1 \ \text{versus} \ 2$, $2 \ \text{versus} \ 3$ and $3 \ \text{versus} \ 4$? Whereas the proportional odds model is cumulative?

Jones
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    Of possible interest: [Multinomial logit](http://en.wikipedia.org/wiki/Multinomial_logit). –  Oct 12 '12 at 18:03
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    The question of which link to use is not very closely related to whether you want to do binary logistic (probit) regression, ordinal regression, or multinomial reg. You may find my answer here: [difference-between-logit-and-probit-models](http://stats.stackexchange.com/questions/20523//30909#30909), helpful in understanding links. Re: the type of model to use, @Procrastinator is pointing you in the right direction. – gung - Reinstate Monica Oct 12 '12 at 18:06
  • It is not clear whether your response variable is ordinal or categorical/nominal. Please clarify! – kjetil b halvorsen Oct 26 '21 at 15:14

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