Hi Mahmood,
I understand you want to give the cumulative probabilities of response categories that are not available in the training data.
An ordered logit model is a multinomial model for ordinal responses with the logit link function.
This model captures the log cumulative odds of a response under the assumption that the effects of predictor variables are the same for all categories on the logarithmic scale. It essentially means that for all categories cj:
Note: Log cumulative odds of a response is the logarithm of the ratio of the probability that the response belongs to a category with a value less than or equal to category j, P(y ≤ cj), and the probability that a response belongs to a category with a value greater than category j, P(y > cj).
From the above formula, we can derive the cumulative probability of a response cj:
You may observe that the cumulative probability depends on the value of alpha (intercept) estimated for that response.
For responses not available in the training data, we cannot estimate the value for the intercept, and hence cannot give the cumulative (or categorical) probability for that response.
However, you can give a lower bound on the cumulative probability of a response ci. For ci > cj (cj being the predecessor of ci in the ordering of response categories):
Refer to the following MATLAB documentation for further reference:
- Multinomial Models for Ordinal Responses: https://www.mathworks.com/help/stats/multinomial-models-for-ordinal-responses.html
- fitmnr: https://www.mathworks.com/help/stats/fitmnr.html
- MultinomialRegression: https://www.mathworks.com/help/stats/multinomialregression.html
