Common mistake 1 with Ordered logit / probit

Running OLS on a 1-to-5 rating instead. That asserts the gap from 1 to 2 equals the gap from 4 to 5, which is exactly the claim you cannot support.

Common mistake 2 with Ordered logit / probit

Accepting proportional odds without looking. If an effect plainly differs at the bottom and the top, a generalised ordered model or a multinomial one is more honest.

Common mistake 3 with Ordered logit / probit

Reading the cut points as substantively interesting. They are nuisance parameters that locate the categories, nothing more.

Common mistake 4 with Ordered logit / probit

Using ordered logit on a categorical variable that merely LOOKS ordered - occupation coded 1 to 5, or a Likert item where the middle category is 'don't know'. Multinomial logit imposes no order and costs only parameters.

EconStatsCraft › Ordered logit / probit

Ordered logit / probit

For an outcome with categories that are ranked but not evenly spaced - a 1-to-5 satisfaction score, a credit rating, low/medium/high. One coefficient per variable describes the shift towards higher categories, with estimated cut points between them.

What it needs

Ordered categorical outcome - Three or more ranked categories.
Independent variables

The intuition

A rating from "strongly disagree" to "strongly agree" has an order but no arithmetic: the gap between agree and strongly agree is not the same size as the gap between neutral and agree, and averaging the numbers 1 to 5 pretends otherwise. Ordered logit posits one underlying continuous attitude cut into bands by thresholds. A regressor shifts the whole attitude left or right, and the thresholds stay where they are.

When to use it

The outcome has three or more categories with a genuine order, and treating the labels as numbers would be a lie about the spacing between them.

Where the estimator comes from

Let y_i^=x_i'\beta+u_i with u_i logistic, observed as category j when \kappa_{j-1}<y_i^\le\kappa_j. Then P(y_i\le j\mid x)=\Lambda(\kappa_j-x_i'\beta), so each CUMULATIVE probability is an ordinary logit with its own intercept and a SHARED slope. That shared slope is the proportional-odds assumption. Note the sign convention: a positive \beta raises y^* and therefore lowers the probability of being at or below any given category. There is no separate constant - the thresholds absorb it, which is why software reports J-1 cut points and no intercept.

The model

P(y\le j\mid \mathbf{x})=F(\kappa_{j}-\mathbf{x}^{\prime}\boldsymbol{\beta}),\qquad \kappa_{1}<\kappa_{2}<\dots<\kappa_{J-1}

What it assumes

Proportional odds: the effect of a variable is the same at every cut point. This is what buys the parsimony and it is the assumption to check.
The categories are genuinely ordered.
The link is correct - logistic or normal.
The categories are genuinely ordered and equally ordered for everyone. A five-point scale where some respondents treat the middle as neutral and others as mildly positive is not one ordered variable, and no amount of estimation will reveal it.

Statistical properties

The coefficient is on the latent variable and is not a probability effect. Its exponential is an odds ratio for being in a higher category, constant across every possible cut point - which is precisely what proportional odds asserts.
Marginal effects differ by category and must sum to zero across categories. A regressor that raises the top category must lower some other one.
Proportional odds is a real restriction and is frequently violated. The Brant test checks it; when it fails, a generalised ordered logit or a multinomial model that ignores the ordering is the alternative.
Ordered probit and ordered logit give coefficients differing by roughly a factor of 1.6 - the ratio of the logistic to the normal standard deviation - and almost identical marginal effects. The choice between them is aesthetic.
Collapsing categories is not innocent. Merging the two top bands changes the thresholds and can change conclusions, so it should be a decision made before looking at results.
Treating the rating as continuous and running OLS is not always wrong for the SIGN of an effect, but it invents a metric and its predictions can fall outside the category range.

How to read the output

A positive coefficient means higher values push the outcome towards the top categories. There is one number per variable, not one per category.
The cut points are where the latent index is sliced. Two nearly equal cut points mean that boundary is barely visible in the data and you might merge those categories.
Compare predicted with observed category shares. Systematic gaps are evidence against proportional odds.
The cut points are nuisance parameters, not findings. They locate the thresholds on the latent scale and are not comparable across samples, so there is nothing to interpret in the fact that one sits at 0.89 and another at 2.14.

A worked reading

A five-point job-satisfaction scale for 900 respondents, with 117 in the lowest category and 126 in the highest. Each additional child lowers the odds of being in a higher category by a factor of 0.5803 - almost halving them - with schooling (odds ratio 1.0925 per year) and husband's income (1.0265 per unit) pulling the other way. The four cut points come out at -0.4875, 0.8885, 2.1368 and 3.4945, and the average predicted probabilities match the observed shares to within a tenth of a percentage point in every category, which is the least a five-category model should manage. Proportional odds is the claim that the single figure 0.5803 applies identically to the odds of clearing the first threshold, the second, the third and the fourth. One number replacing four is what the model buys, and it is an assumption rather than a finding: if the effect of children really differs between the bottom of the scale and the top, the summary is a fiction and only a test of parallel lines will say so.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Brant test rejecting	Proportional odds fails	Use a generalised ordered model, or report multinomial
A threshold not increasing	An estimation failure	Cut points must be ordered by construction
Very few observations in one category	That threshold is poorly identified	Consider merging, deciding before you see results
Coefficient signs the reverse of expectation	The software's sign convention	Check whether it models P(y <= j) or P(y > j)
Odds ratio enormous	Near-perfect separation in a small category	Check the crosstab
Marginal effects not summing to zero	An arithmetic error	They must, across all categories

Common mistakes

Running OLS on a 1-to-5 rating instead. That asserts the gap from 1 to 2 equals the gap from 4 to 5, which is exactly the claim you cannot support.
Accepting proportional odds without looking. If an effect plainly differs at the bottom and the top, a generalised ordered model or a multinomial one is more honest.
Reading the cut points as substantively interesting. They are nuisance parameters that locate the categories, nothing more.
Using ordered logit on a categorical variable that merely LOOKS ordered - occupation coded 1 to 5, or a Likert item where the middle category is 'don't know'. Multinomial logit imposes no order and costs only parameters.

Where to read this properly

McCullagh (1980), "Regression Models for Ordinal Data", JRSS-B 42(2).
Brant (1990), "Assessing Proportionality in the Proportional Odds Model", Biometrics 46(4).
Long and Freese, Regression Models for Categorical Dependent Variables Using Stata (2014), ch. 7.
Wooldridge, Econometric Analysis of Cross Section and Panel Data (2010), ch. 16.

Related Regression

Multiple regression (OLS) · Logit / Probit · Tobit (censored) · Truncated regression · Multinomial logit · Quantile regression · Poisson / Negative binomial

All analyses

Data & variables

Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

Filter variables

Drag a variable into a slot on the right - or just click it.

Choose an example dataset above to begin.

Choose a transformation - it opens in the data editor, with a live preview.

Apply to

Multiply by

Columns ctrl-click for several

Group by ctrl-click for several

Within groups

Statistic

Bands

How many

Cut points

Keep rows where

Value

and

Fill with

Value

Also mark which rows were filled

Rules

Base period = 100

Which part

Percent at each tail

Threshold

Survey weight optional

Direction

Names column

Values column

Largest first

Delete them, not just count them

Read this column as

Tidy the text

New name optional

EconStatsCraft rigorous, plain-spoken econometrics

Econometrics that explains itself.

Regression, panel data, time series and the whole battery of tests. Every result is followed by a verdict you can defend.

Load a dataset to see it here.

Ordered logit / probit

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

Related Regression

All analyses

Charts

Maps

Explore

Regression

Time series - one series

Time series - several series

Panel data

Multivariate statistics

Marketing research

Causal

Finance & risk

Actuarial

Tests & breaks

Machine learning

Econometrics that explains itself.