Polytomous Logistic Regression models look at cumulative frequencies.
Table 1: Observed Frequencies
Table 2: Observed Proportions - the observed frequencies converted into percentages
Table 3: Observed Cumulative Proportions - the observed proportions accumulated across rows.
All three of these tables are simply descriptive. Now, we can look at Table 3 where the proportions have been accumulated and look for values that are lower in the higher rating ranges. So, just looking at the data in this was can you determine which ice cream fat level is the best? Can you tell? What are you looking for?
Table 4: Fitted Cumulative Probabilities
What about looking at the Fitted cumulative probabilites in the table above? How does this help you determine which ice cream fat level is the best? Can you tell? What are you looking for?
How does this compare if we just used a simple average of the ratings? Here is a table of the average ratings for each fat level and a plot of a quadratic regression of this data.
How does this help us understand this problem? Should you stop here?
The Quadratic Nature of the Responses
Many examples of polytomous regression are linear in nature. Why is this example quadratic in nature?