# Solved – Proportional hazards vs proportional odds for modeling ordinal data

When working with ordinal response data, we can use a proportional odds model to calculate the log odds in favor of one category over another. Often we use a logit link yielding the following model:

$${rm logit}big(P(Y leq j|bf{x})big) = alpha_j + bf{x'beta}$$

for $$j = 1, …, J$$ responses.

Alternatively, I've seen it formulated as a proportional hazards model, which is basically the same model, except we use an Extreme Value Function ($$F(x) = 1 – e^{-e^{-x}}$$) as the link:

$$log(-log(1 – P(Y leq j|{bf x})) = alpha_j + bf{x'beta}$$

From empirical analysis, I see that my coefficients and resulting fits are similar in both cases.

Question:

1. Can someone intuitively explain the connection between this proportional hazards model for calculating the odds of an ordinal response, and the proportional hazards model for determining survival probabilities via a hazard function?

Note that I have a mathematical derivation of how a hazard function fits in the proportional hazard model, but the connection between the two seemingly different types of problems eludes me.

2. Is there a situation when one model is preferred over another for ordinal response data (other than just that a logit link is more interpretable than the extreme value link)?

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