Question

Briefly explain the difference between an ordinal logit model and a multinomial logit model.

Answer 1

The multinomial logistic regression has no intrinsic ordering; on the other hand a ordinal regression has a link between the levels. For instance, if we investigate the variable V1 that has green; yellow ; red as autonomous levels in this case V1 encodes a multinomial variable. If we have a another variable V2 were the levels green; yellow ; red denote some kind of increased urgency then they identify as an ordinal variable.

A multinomial variable is encoded as an indicator matrix. The encoding for green = [1 0 0], yellow is [0 1 0] & red is [0 0 1] . For an ordinal variable the encoding is a little different. If we are in the yellow level we have assumed that we have attained & exceed the green level. Similarly if we are in the red level we have attained the green & yellow level and now we are in the red level. Thus, the encoding for the green value would be somewhat like [1 0 0]. For the yellow value, [1 1 0] & for red, [1 1 1].