SPSS command: SPSS CATREG

Categorical regression with optimal scaling

Categorical regression fits a linear regression after converting nominal and ordinal categories into optimal numeric values, so a rating outcome or a region predictor needs no arbitrary coding.

Run Categorical Regression (CATREG) in your browser All SPSS procedures

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

What it tells you

Crosstabs runs the SPSS CATREG procedure in your browser by alternating least squares, reporting R², standardized coefficients, Pratt importance and the category quantifications.

How much of the variance of the quantified outcome the scaled predictors explain (multiple R, R², apparent prediction error).
Each predictor's standardized beta and its zero-order, partial and part correlations.
Which predictor matters most, by Pratt's relative importance (the importances sum to 1).
How each category is scaled — for example whether satisfaction rises evenly with tenure or levels off.

When to use it

Use it when

An ordinal outcome such as a 1–5 satisfaction rating with a mix of nominal, ordinal and numeric predictors.
Nominal predictors with many categories where dummy coding would produce a long, hard-to-read coefficient list.
Driver analysis: ranking predictors by importance when relationships may be nonlinear.

Use something else when

You need confidence intervals, p values or predicted category probabilities: ordinal or multinomial logistic regression provide them; the panel computes no bootstrap standard errors or F tests.
A continuous outcome with linear effects: ordinary linear regression is simpler and gives full inference.
You need spline transformations, regularization (ridge, lasso, elastic net) or passive missing-value handling: these are not included.

How to run it in Crosstabs

01
Open your data
Open a .sav, CSV or Excel file in the workspace and switch to Statistics mode. The file is read in your browser.
02
Choose Categorical regression
In the Regression group, pick Categorical regression (CATREG).
03
Set the dependent variable
Choose the Dependent variable and its Scaling level (Nominal, Ordinal or Numeric). Variables with 2–40 categories are listed.
04
Give predictors scaling levels
Under Independent variables and their scaling levels, set each predictor you want to Nominal, Ordinal or Numeric; leave others on Not used.
05
Run
Set Maximum iterations if needed (default 100) and click Run categorical regression. Cases with any missing value are excluded listwise; a weight acts as a replication weight.

Run Categorical Regression (CATREG) in your browser

Worked example

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

Data

180 synthetic customers with an ordinal satisfaction rating (1–5), region (four regions, nominal), tenure in years (1–5, ordinal) and the number of support contacts (0–4, numeric). Satisfaction was simulated to differ by region in no particular order, to rise steeply over the first years of tenure and then level off, and to fall with each support contact. Seed fixed.

Model Summary

Multiple R	R Square	Apparent Prediction Error
0.778	0.606	0.394

Dependent variable: satisfaction (ordinal). 180 cases used; 7 iterations.

Coefficients

Variable	Standardized Beta
region	0.388
tenure	0.610
contacts	−0.273

Bootstrap standard errors and F tests are not computed.

Correlations and Tolerance

Variable	Zero-Order	Partial	Part	Importance	Tolerance (after transformation)
region	0.384	0.523	0.385	0.246	0.986
tenure	0.636	0.696	0.609	0.640	0.996
contacts	−0.252	−0.397	−0.272	0.114	0.986

Importance is Pratt's measure: beta × zero-order correlation / R². Importances sum to 1.

Quantifications: region

Category	Frequency	Quantification
Central	44	0.080
Coast	47	1.269
Mountain	37	−1.677
Valley	52	−0.021

Optimal scaling level: Nominal.

How to read it

The optimally scaled predictors explain 60.6% of the variance in the quantified satisfaction (R = 0.778). Tenure is the most important predictor (Pratt importance 0.640). Region needs no ordering: its quantifications place Coast highest and Mountain lowest. Tenure, scaled ordinally, gets quantifications from −1.70 (year 1) to 0.73 (year 5), and 57% of that rise falls between year 1 and year 2 — a curve that equal-interval coding would flatten.

Output tables explained

Model Summary: Multiple R, R Square and the apparent prediction error (1 − R²), with the cases used and the number of iterations.
Coefficients: Standardized beta for each predictor on its optimally scaled values.
Correlations and Tolerance: Zero-order, partial and part correlations, Pratt importance (beta × zero-order correlation / R²) and tolerance after transformation; low tolerance signals collinearity.
Quantifications: {variable}: For the outcome and every predictor, each category's frequency and the numeric value it receives.

Assumptions and notes

After transformation the model is a linear regression: effects are additive across predictors, with no interactions.
Nominal levels with many sparse categories can overfit; R² is an in-sample (apparent) measure, not a validated one.
The response cannot also be a predictor, and every variable needs at least two categories among complete cases.

How the results are validated

Reference values come from an independent numpy implementation of the SPSS CATREG alternating-least-squares scheme. With numeric levels it matches statsmodels OLS (R² to about 3e-16, betas to about 1e-8), and its R² for nominal and mixed models agrees with R Gifi::morals to about 3e-11. Tests on numeric, frequency-weighted numeric, nominal and mixed models require R², multiple R and apparent prediction error within 1e-10, betas, correlations, importance and tolerance within 1e-6, and quantifications within 1e-5. Validation evidence

Questions

How do I read the R² of a categorical regression?

It is the share of variance of the quantified outcome explained by the quantified predictors. Because the quantifications are chosen to maximize fit, it is optimistic — usually higher than the R² of a linear regression on the raw codes.

What is Pratt's importance?

Beta multiplied by the zero-order correlation, divided by R². The values sum to 1, so each one is the predictor's share of the explained variance; a negative importance signals suppression.

Why are there no p values?

SPSS CATREG can report standard errors and F tests for the coefficients; this panel does not compute them, as the footnote under Coefficients says. Use the coefficients and importances descriptively, or confirm key effects with ordinal or linear regression.

Nominal, ordinal or numeric — what difference does it make?

Numeric keeps the original spacing, so it reproduces linear regression on standardized variables. Ordinal keeps only the order and can capture a curve; nominal lets categories take any values, which suits unordered predictors like region.

Run Categorical Regression (CATREG) 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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