SPSS command: SPSS PLUM

Ordinal regression (PLUM) in your browser

Q: Why are the signs in PLUM opposite to some other software?

PLUM writes the model as link(P(Y ≤ j)) = threshold − location, so a positive coefficient means higher categories become more likely. Some packages use threshold + location and report the opposite sign for the same fit.

Q: Which link function should I use?

Logit is the usual default and gives odds ratios. Probit suits a normally distributed latent variable, complementary log-log suits outcomes where higher categories are more likely, negative log-log where lower ones are, and cauchit data with extreme values. Compare −2 log likelihood across links on the same data.

Q: What if the test of parallel lines is significant?

The effects probably differ across thresholds. With large samples the test rejects small departures, so also check whether conclusions change in separate binary splits; if they do, multinomial regression is safer.

Q: How do I turn estimates into odds ratios?

With the logit link, exp(estimate) is the odds ratio of being in a higher rather than a lower category for a one-unit increase (or versus the reference level of a factor). The panel shows the estimates and their confidence limits; exponentiate both ends for the odds-ratio interval.

Ordinal regression models an outcome whose categories have a natural order — satisfaction ratings, severity grades, education levels — through cumulative probabilities that share one set of slopes.

Try with example data Run on your own file

Free · No account · Files stay on your device · Updated 18 October 2026

Worked example result

Model Fitting Information · Final

Chi-Square(2) = 48.862

p <.001

Model	-2 Log Likelihood	Chi-Square	df
Intercept Only	430.870
Final	382.008	48.862	2

Model Fitting Information

See the full worked example

What it tells you

Crosstabs runs the SPSS PLUM procedure on your device with logit, probit, complementary log-log, negative log-log and cauchit links, and tests the proportional-odds assumption with the test of parallel lines.

Whether the predictors improve on the thresholds-only model (Model Fitting Information, likelihood-ratio chi-square).
The direction and size of each predictor's effect on the latent ordered outcome (Location estimates with Wald tests and confidence intervals).
Where the cut points between adjacent categories lie on the latent scale (Threshold estimates).
Whether one set of slopes fits every cumulative split, via the test of parallel lines against the general model.

When to use it

Use it when

A Likert item, rating scale or graded outcome with three to about ten ordered categories.
You want one effect per predictor rather than a separate logit for each category, as multinomial regression would give.
You want to compare link functions — for example complementary log-log when higher categories are more probable.

Use something else when

The categories have no order: use multinomial logistic regression.
The outcome has many levels and behaves like a continuous score: linear regression is simpler and easier to report.
The test of parallel lines is clearly rejected and the effects differ by threshold: consider multinomial regression or separate binary models.
You need scale (heteroscedasticity) terms or interactions: this panel fits a location-only main-effects model.

How to run it in Crosstabs

01
Open your data
Open your file in the workspace and switch to Statistics mode. Ordered codes such as 1–5 sort numerically, so category order follows the values.
02
Choose Ordinal regression
In the Regression group, pick Ordinal regression (PLUM).
03
Set the ordinal dependent and link
Choose the Dependent variable (ordinal) and a Link function: Logit, Probit, Complementary Log-log, Negative Log-log or Cauchit.
04
Add predictors
Tick categorical predictors under Factors and numeric ones under Covariates.
05
Set options and run
Under Options keep Test of parallel lines ticked, set Confidence level (%) and click Run.

Run Ordinal Regression in your browser

Worked example

Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.

Try with example data

Data

160 synthetic support contacts rate satisfaction on a 1–4 scale. Each rating comes from a logistic latent score that falls with wait (minutes) and is higher for Chat than Phone, cut at three fixed thresholds; the seed is fixed.

Model Fitting Information

Model	-2 Log Likelihood	Chi-Square	df	Sig.
Intercept Only	430.870
Final	382.008	48.862	2	<.001

Parameter Estimates

Item	Category	Estimate	Std. Error	Wald	Sig.	Lower Bound	Upper Bound
Threshold	[satisfaction = 1]	−3.676	0.462	63.195	<.001	−4.582	−2.769
	[satisfaction = 2]	−2.490	0.412	36.459	<.001	−3.298	−1.682
	[satisfaction = 3]	−1.107	0.366	9.160	.002	−1.825	−0.390
Location	[channel=Chat]	0.418	0.299	1.948	.163	−0.169	1.005
	wait	−0.265	0.041	41.199	<.001	−0.346	−0.184

Link function: Logit. The redundant [channel=Phone] row is omitted.

Test of Parallel Lines

Model	-2 Log Likelihood	Chi-Square	df	Sig.
Null Hypothesis	382.008
General	379.634	2.374	4	.667

How to read it

Wait time and channel improve on the thresholds-only model by χ²(2) = 48.86, p < .001, Nagelkerke R² = 0.282. Each extra minute of waiting shifts the latent score by −0.265, so the odds of a rating at or above any level fall by a factor of 0.767 per minute; Chat users sit 0.418 logits higher than Phone users (odds ratio 1.52, p = .163), a difference this sample cannot distinguish from zero. The test of parallel lines is not significant (χ² = 2.37, p = .667), so one set of slopes for all thresholds is adequate.

Output tables explained

Step Summary: With a stepwise method: the starting model, then each effect entered or removed with the model's AIC, BIC and −2 log likelihood and the chi-square, df and significance of the entry or removal test.
Model Fitting Information: −2 log likelihood of the thresholds-only (Intercept Only) and final models with the likelihood-ratio chi-square, df and significance.
Goodness-of-Fit: Pearson and deviance chi-square over covariate patterns; with continuous covariates many cells are empty and these tests lose meaning, which the case summary notes.
Pseudo R-Square: Cox and Snell, Nagelkerke and McFadden measures of improvement over the thresholds-only model.
Parameter Estimates: Threshold rows give the cut points; Location rows give predictor effects. A positive location estimate shifts cases toward higher categories.
Test of Parallel Lines: Compares the model with a general model whose slopes differ by threshold; a non-significant result supports the proportional-odds (parallel lines) assumption.

Assumptions and notes

Proportional odds (parallel lines): each predictor has the same effect at every cumulative split of the outcome.
The outcome categories are genuinely ordered and the chosen link fits the shape of the cumulative probabilities.
Independent observations and no complete separation between predictors and outcome categories.
At most 30 outcome categories; missing values are excluded listwise and only frequency weights are accepted.

How the results are validated

PLUM is tested against R ordinal::clm for the logit, probit, complementary log-log and negative log-log links and a frequency-weighted logit model: thresholds and location estimates agree within 1e-6, their standard errors within 1e-5, −2 log likelihood within 1e-8 and the general model behind the test of parallel lines within 1e-6. The cauchit link is checked against statsmodels OrderedModel (estimates within 1e-6, standard errors within 1e-4, −2LL within 1e-9). Validation evidence

Questions

Why are the signs in PLUM opposite to some other software?

PLUM writes the model as link(P(Y ≤ j)) = threshold − location, so a positive coefficient means higher categories become more likely. Some packages use threshold + location and report the opposite sign for the same fit.

Which link function should I use?

Logit is the usual default and gives odds ratios. Probit suits a normally distributed latent variable, complementary log-log suits outcomes where higher categories are more likely, negative log-log where lower ones are, and cauchit data with extreme values. Compare −2 log likelihood across links on the same data.

What if the test of parallel lines is significant?

The effects probably differ across thresholds. With large samples the test rejects small departures, so also check whether conclusions change in separate binary splits; if they do, multinomial regression is safer.

How do I turn estimates into odds ratios?

With the logit link, exp(estimate) is the odds ratio of being in a higher rather than a lower category for a one-unit increase (or versus the reference level of a factor). The panel shows the estimates and their confidence limits; exponentiate both ends for the odds-ratio interval.

Run Ordinal Regression on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

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