# Where is there is only set of odds ratio in ordinal logistic regression?

I am running an ordinal logit regression with health status(poor, fair, good, very good, excellent) as the outcome. I understand the difference between ordinal and multinomial outcomes, and read many tutorials about the proportional odds assumption. But none were plain enough for me to understand how that works, and how/why the model produces only 1 set of odds ratios.

Below is the closest explanation I have found, but it still doesn't clarify the process of producing only 1 set of odds ratios:

The probability of a person's health being in the "Poor or below" category, which includes the "Poor", "Fair", and "Good" categories. This is compared to the reference category of "Excellent or above". The probability of a person's health being in the "Fair or below" category, which includes "Poor", "Fair", "Good", and "Very Good". This is compared to the reference category of "Excellent". The probability of a person's health being in the "Good or below" category, which includes "Poor", "Fair", and "Good". This is compared to the reference category of "Excellent or above". The probability of a person's health being in the "Very Good or below" category, which includes "Poor", "Fair", "Good", and "Very Good". This is compared to the reference category of "Excellent". The probability of a person's health being in the "Excellent" category. This is the reference category.

This question was asked and answered in many instances before, but I hope someone can help clarify this in plain English using this example. Thank you in advance!

This is explained in detail here (start with the first link to BBR). If you want to allow ratios of odds of $$Y \geq y$$ to vary with $$y$$ without restriction, use the polytomous (multinomial) logistic regression model. This requires a much larger sample size, e.g., the size of the smallest cell of $$Y$$ needs to be large. Proportional odds and proportional hazards and other semiparametric ordinal models requires an overall large-enough sample size and there to be no more than say $$\frac{4}{5}$$ of the observations at any one level of $$Y$$ unless the overall $$N$$ is large. Sample size issues are covered in one of the links in the first link I provided at the top, and here.