SPSS command: SPSS GENLIN
Generalized linear models (GENLIN) in your browser
A generalized linear model links the mean of an outcome to predictors through a link function and lets the outcome follow a distribution other than the normal — counts, positive skewed costs, proportions or yes/no events.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS GENLIN procedure on your device with seven distributions, a choice of links and scale methods, Type III Wald or likelihood-ratio tests, robust standard errors, and generalized estimating equations for repeated or clustered data.
- Whether the model as a whole beats the intercept-only model (Omnibus Test, likelihood-ratio chi-square).
- Which effects matter, with Type III Wald or likelihood-ratio chi-square tests per factor and covariate.
- Effect sizes on the response scale through Exp(B) — rate ratios for Poisson and negative binomial, odds ratios for a binomial logit, ratios of means for a log link.
- Whether the chosen distribution fits: deviance and Pearson chi-square per df flag overdispersion, and AIC, AICC, BIC and CAIC compare candidate models.
- With GEE, population-averaged effects for repeated measures, the estimated working correlation and the QIC and QICC criteria.
When to use it
Use it when
- Counts such as tickets, visits or defects (Poisson, or negative binomial when the variance exceeds the mean).
- Positive, right-skewed amounts such as claim costs or durations (gamma or inverse Gaussian, usually with a log link), or amounts with exact zeros (Tweedie).
- Binary outcomes or events out of trials, when you want a logit, probit, log or complementary log-log link in one framework.
- Repeated measurements of the same subjects, analysed with GEE and an exchangeable, AR(1) or unstructured working correlation.
Use something else when
- A continuous, roughly normal outcome with a few predictors: linear regression or GLM Univariate give the same estimates with familiar output.
- You need subject-specific random effects rather than population-averaged effects: use linear mixed models.
- You need interaction terms: the panel fits main effects of factors and covariates only.
- Frequency weights together with GEE: the repeated-measures model refuses them, so expand or clear the weight first.
How to run it in Crosstabs
- 01
Choose Generalized linear models
Open your data in Statistics mode and, in the General linear model group, pick Generalized linear models (GENLIN).
- 02
Pick the type of model
Under Type of model choose the Distribution and a Link function; the list of links follows the distribution. Set Power for a power link, Tweedie power (1–2) for Tweedie, and Negative binomial parameter k (Estimate value or Specify value).
- 03
Set the response and predictors
For the binomial, set Response format to Binary (two categories) with a Reference category, or Number of events / trials with the Number of trials variable. Then choose the Dependent variable and tick Factors and Covariates.
- 04
Choose estimation and output
Under Estimation and output set Include intercept, the Scale parameter method (Maximum likelihood estimate, Fixed value (1), Deviance or Pearson chi-square), Robust (sandwich) standard errors, the Type III test statistic (Wald or Likelihood ratio) and Include exponential parameter estimates.
- 05
Add repeated measures if needed
Tick Use generalized estimating equations, choose the Subject variable, an optional Within-subject variable, the Working correlation matrix (Independent, Exchangeable, AR(1), Unstructured) and the Covariance matrix (Robust estimator or Model-based estimator), then click Run.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
120 synthetic customer accounts on three plans (Free, Plus, Team) with 5–50 seats. Monthly support tickets are Poisson counts whose log mean rises with seats and is highest on Free; the seed is fixed. Distribution = Poisson, Link function = Log, Include exponential parameter estimates is ticked.
| Item | Value | df | Value/df |
|---|---|---|---|
| Deviance | 148.109 | 116 | 1.277 |
| Pearson Chi-Square | 135.849 | 116 | 1.171 |
| Log Likelihood | −249.115 | ||
| Akaike's Information Criterion (AIC) | 506.230 | ||
| Bayesian Information Criterion (BIC) | 517.380 |
| Likelihood Ratio Chi-Square | df | Sig. |
|---|---|---|
| 57.502 | 3 | <.001 |
| Source | Wald Chi-Square | df | Sig. |
|---|---|---|---|
| (Intercept) | 25.690 | 1 | <.001 |
| plan | 14.207 | 2 | <.001 |
| seats | 33.782 | 1 | <.001 |
| Parameter | B | Std. Error | Wald Chi-Square | Sig. | Exp(B) | 95% Wald Confidence Interval for Exp(B) Lower | 95% Wald Confidence Interval for Exp(B) Upper |
|---|---|---|---|---|---|---|---|
| (Intercept) | 0.411 | 0.147 | 7.773 | .005 | 1.509 | 1.130 | 2.014 |
| [plan=Free] | 0.452 | 0.120 | 14.207 | <.001 | 1.571 | 1.242 | 1.987 |
| [plan=Plus] | 0.286 | 0.124 | 5.295 | .021 | 1.331 | 1.043 | 1.698 |
| seats | 0.022 | 0.004 | 33.782 | <.001 | 1.023 | 1.015 | 1.030 |
Team is the reference plan; its redundant row and the fixed (Scale) = 1 row are omitted.
How to read it
The Poisson model improves on the intercept-only model by likelihood-ratio χ²(3) = 57.50, p < .001. Deviance/df = 1.277 and Pearson/df = 1.171 are close to 1, so overdispersion is not a concern. Each extra seat multiplies the expected ticket count by 1.023; the plan effect is significant overall (Wald χ²(2) = 14.21, p < .001), and Free accounts file 1.57 times as many tickets as Team accounts of the same size.
Output tables explained
- Model Information
- Dependent variable, probability distribution and link function actually fitted, including the event and reference categories for a binary response.
- Goodness of Fit
- Deviance, scaled deviance, Pearson chi-square and their value/df, log likelihood, and AIC, AICC, BIC and CAIC in smaller-is-better form. Value/df well above 1 for Poisson suggests overdispersion.
- Omnibus Test
- Likelihood-ratio chi-square comparing the fitted model with the intercept-only model.
- Tests of Model Effects
- Type III Wald or likelihood-ratio chi-square for each factor and covariate, with df and significance.
- Parameter Estimates
- B, standard error, Wald confidence interval and hypothesis test per parameter, the scale or negative binomial k row, and Exp(B) with its interval when requested.
- Working Correlation Matrix
- With GEE: the estimated correlation between measurement occasions under the chosen structure, alongside the Correlated Data Summary and QIC/QICC in Goodness of Fit.
Assumptions and notes
- The variance follows the chosen distribution's mean–variance relation (for example variance = mean for Poisson); check deviance/df and switch to negative binomial or a Pearson scale if it is far above 1.
- The link makes predictors act linearly on the transformed mean; responses outside the distribution's range (negative counts, zero for gamma) are excluded with a note.
- Observations are independent, or, with GEE, independent between subjects with correlation allowed within a subject.
- Maximum-likelihood scale estimation applies only to the normal, gamma, inverse Gaussian and Tweedie distributions.
How the results are validated
GENLIN is compared with statsmodels GLM and, for the negative binomial and Tweedie models, R MASS::glm.nb and statmod/tweedie. The tests cover Poisson (with ML, deviance and Pearson scale, robust SEs and frequency weights), gamma, inverse Gaussian, normal, binary logit, events/trials probit, negative binomial with estimated and fixed k, and Tweedie 1.5: log likelihood and information criteria agree within 1e-9, deviance and Pearson chi-square within 1e-8, and robust standard errors within 1e-6. GEE is checked against statsmodels GEE and a NumPy implementation of SPSS's moment estimators: coefficients within 1e-8, robust SEs within 1e-7, working correlations within 1e-8 and QIC/QICC within 1e-7. Validation evidence
Questions
Poisson or negative binomial for count data?
Start with Poisson and look at Deviance and Pearson value/df in Goodness of Fit. Values well above 1 mean the counts vary more than Poisson allows; refit with Negative binomial (k estimated) and compare AIC, or keep Poisson with a Pearson scale.
How do I model a rate, such as tickets per seat?
The panel has no offset field. Enter the log of exposure as a covariate in a log-link Poisson model; its coefficient estimates the exposure effect instead of fixing it at 1. For a binomial proportion, use Number of events / trials.
What does Exp(B) mean with a log link?
It is a ratio of expected values: 1.25 means the mean count (or amount) is 25% higher for a one-unit increase, or for that factor level versus the reference level, with other predictors fixed.
When should I use GEE instead of the ordinary model?
When the same subject contributes several rows — repeated visits, waves of a panel, patients within clinics. GEE keeps the GLM mean model but uses a working correlation and robust standard errors, so inference accounts for the clustering.
Wald or likelihood-ratio Type III tests?
Likelihood-ratio tests refit the model without each effect and behave better in small samples or near boundaries; Wald tests are faster and are the default. With GEE only Wald tests are available.
Related procedures
- GLM UnivariateUNIANOVA
- Binary Logistic RegressionLOGISTIC REGRESSION
- Linear Mixed ModelsMIXED
- Probit AnalysisPROBIT
- General Loglinear AnalysisGENLOG
- Complex Samples General Linear ModelCSGLM
- Free SPSS alternative: full coverage list
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