Ordinal regression models an ordered outcome — poor, fair, good; disagree, neutral, agree — by estimating the odds of being above each cutpoint, with one shared coefficient per predictor. That sharing is the proportional-odds assumption, and it is what makes the output compact enough to read. It is also the thing most likely to be wrong, and it is cheap to test: fit the binary models the assumption says are equal and see whether they are.
The assumption underneath the single coefficient
An ordinal model with three categories has two cutpoints: poor against fair-or-good, and poor-or-fair against good. Each is a perfectly ordinary binary question, and each could have its own coefficient. Proportional odds is the decision to give them one coefficient between them.
That is why the output is compact and readable. It is also a testable claim about the data, and the cheapest test is the most direct one: fit the two binary models separately and compare. On the first preset they come back 0.4457 and 0.4508, a spread of 0.0050, and the parallel-lines test returns p = 0.8260. Pooling has cost nothing.
On the second preset they come back 0.4171 and 0.9866. Waiting time barely moves a customer from poor to fair and moves them substantially from fair to good, and those are genuinely different effects. The pooled coefficient is 0.7052 — between the two, describing neither — and it reports a p-value of 2.46e-16 and an odds ratio of 2.02. A reader given only that line would conclude the effect is strong, precisely estimated, and uniform.
The parallel-lines test catches it at p = 0.0000, which is why the test runs on every input here rather than being an option. The failure mode is not that the model breaks loudly; it is that it reports something clean and wrong.
What to do when it fails
A rejected parallel-lines test is not a reason to abandon the analysis. The separate fits in the table are themselves the answer — report 0.4171 for the first step and 0.9866 for the second, and say that the effect is concentrated in the upper step. That is more information than the pooled coefficient, not less.
A partial proportional-odds model formalises that: share the coefficient across cutpoints for predictors where the assumption holds, free it for the ones where it does not. It sits between the two extremes and is the right answer reasonably often, at the cost of a model whose output takes longer to explain.
The other route is to give up the ordering entirely and fit a multinomial model, which assumes nothing about the order and estimates a separate coefficient vector per category. That always fits at least as well and costs a great deal of precision, since it is estimating far more parameters from the same rows. Worth it when the categories are not really ordered; wasteful when they are.
One warning about sample size. The test needs enough rows in every category to estimate the separate fits, and with a sparse top category it has very little power — so a passing test on an unbalanced outcome is weak evidence. The category counts are printed beside the thresholds for exactly that reason.
Reading the coefficient
The odds ratio is for being in a higher category rather than for any particular category. An odds ratio of 1.58 means each extra unit of the predictor multiplies the odds of being above any given cutpoint by 1.58 — not that it raises the probability of the top category by 58%, which is the usual misreading.
The thresholds are cut points on an unobserved continuous scale and come back strictly increasing because the categories are ordered. They are rarely worth interpreting: they carry the marginal distribution of the categories and little else. Two studies with identical predictor effects and different category frequencies will have quite different thresholds.
The direction convention matters and differs between software packages. Here a positive coefficient means higher values of the predictor push toward higher categories, which is the reading most people expect. Some packages report the opposite sign for the same fit, so a coefficient copied between tools without checking is a common source of a reversed conclusion.
Treating the categories as numbers
The most common alternative to this model is not another model, it is ordinary least squares on the category codes — running a regression with the outcome coded 1, 2, 3. It is quick, the coefficient is easy to describe, and it asserts something the data does not support: that the step from poor to fair is the same size as the step from fair to good.
Ordinal codes carry order and nothing else. The distance between them is an artefact of the coding, and multiplying by a coefficient treats that artefact as a measurement. Recode the same categories as 1, 2, 5 and the least squares answer changes; the ordinal model’s answer does not change at all, because it uses only the ordering.
With many categories and roughly even spacing the two approaches often agree closely, which is why the shortcut survives. With few categories, uneven spacing, or a piled-up end of the scale, they do not, and the ordinal model is the one making the smaller assumption.
Reporting it
Report the parallel-lines test result with the coefficient, and report the separate cutpoint fits whenever the test rejects. A coefficient presented without any statement about the assumption it rests on is not interpretable, and on the second preset it would be actively misleading.
Give the category counts. They tell a reader how much power the assumption test had, and a passing test on an outcome where the top category holds nine observations is not evidence of anything. State the sign convention you are using. And where the assumption fails and you have reported the separate fits, say which step the effect is concentrated in — that is usually the substantive finding, and pooling destroys it.
Sources and methodology
References for the model and for testing its central assumption.
Method. The proportional-odds likelihood is maximised by Newton steps with a numerically differentiated Hessian and a backtracking line search, and standard errors come from the observed information. The separate cutpoint fits are ordinary binary logistic regressions by iteratively reweighted least squares, and the parallel-lines statistic is twice the gap between their combined log-likelihood and the constrained one. The suite checks the degenerate case exactly: with two categories the model must reduce to binary logistic regression, and it agrees to 1.1e-10, while on a two-by-two table the coefficient equals the log odds ratio in closed form. It further confirms the thresholds come back strictly increasing, the odds ratios are the exponentials of the coefficients, and the test stays quiet when the assumption holds while firing when it is violated. That engine is verified on every change against 490 assertions. The count and the per-case breakdown are published on the formula verification page.