SPSS command: SPSS META REGRESSION
Meta-regression in your browser
Meta-regression asks whether study-level characteristics, such as dose, year or design, explain why effect sizes differ between studies.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS META REGRESSION procedure on your device with continuous and categorical moderators, random effects under seven τ² estimators or fixed effects with or without a dispersion parameter, Knapp-Hartung tests, residual heterogeneity and R².
- How much the expected effect size changes per unit of each moderator, with standard errors, tests and intervals.
- Whether the moderators jointly explain variation in effects (Wald χ² or, with Knapp-Hartung, F test).
- How much heterogeneity remains after the moderators: residual Q, τ², I² and H².
- The share of between-study variance the moderators explain (R²) in random-effects models.
When to use it
Use it when
- A meta-analysis shows substantial heterogeneity and you have a prespecified hypothesis about its source.
- Testing a dose-response relationship across trials that used different doses.
- Comparing subgroups of studies (e.g. randomized versus observational) with a categorical moderator.
Use something else when
- Fewer than about ten studies per moderator: estimates are unstable and false positives are common.
- You only need the pooled effect: use the binary or continuous meta-analysis.
- You want to infer individual-level effects from study averages: that is the ecological fallacy; you need individual data.
How to run it in Crosstabs
- 01
Enter one row per study
Prepare a file with each study's effect size, its standard error and the moderators, then open it and switch to Statistics mode.
- 02
Choose Meta-Regression
In the Agreement and diagnostics group, pick Meta-Regression (META REGRESSION).
- 03
Set effect size and standard error
Choose the Effect size and Standard error columns; rows with a non-positive standard error are dropped.
- 04
Add moderators
Tick up to eight Covariates (continuous moderators) and up to four Factors (categorical moderators, last category is the reference). At least one moderator is required.
- 05
Pick the model and tests
Set Model to Random effects, Fixed effect or Fixed effect with multiplicative dispersion. For random effects choose the τ² estimator and optionally Knapp-Hartung adjustment (with Truncate the Knapp-Hartung factor at 1); otherwise you may tick Use t distribution (N − p df).
- 06
Run
Set the Confidence level (%) and press Run. You need more studies than model parameters.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
12 synthetic studies of a training programme. Each row holds a precomputed effect size, its standard error and the programme's weekly training hours (1–6). True effects rise by 0.08 per hour, plus between-study variation (SD 0.2) and sampling error, drawn with a fixed seed.
Input preview
| Study | Effect size | Standard error | hours |
|---|---|---|---|
| 1 | 0.052 | 0.110 | 1 |
| 2 | −0.185 | 0.108 | 2 |
| 3 | −0.006 | 0.204 | 3 |
| 4 | 0.352 | 0.189 | 4 |
| 5 | 0.666 | 0.153 | 5 |
| 6 | 0.563 | 0.161 | 6 |
| Parameter | Coefficient | Std. Error | z | Sig. | 95% CI |
|---|---|---|---|---|---|
| Intercept | −0.099 | 0.147 | −0.68 | .499 | −0.386 – 0.188 |
| hours | 0.111 | 0.039 | 2.87 | .004 | 0.035 – 0.186 |
Random-effects meta-regression; τ² estimated by restricted maximum likelihood (REML).
| Item | Statistic | df | Sig. |
|---|---|---|---|
| Model test (Wald χ²) | 8.215 | 1 | .004 |
| Residual homogeneity (Q) | 20.997 | 10 | .021 |
| τ² | 0.0255 | ||
| I² (%) | 52.3 | ||
| H² | 2.096 | ||
| R² (%) | 55.4 |
R² is the share of between-study variance explained by the moderators relative to the intercept-only model.
How to read it
Each extra weekly training hour adds 0.111 to the expected effect size (95% CI 0.035 – 0.186, p = .004); the omnibus Wald test of the moderator is χ²(1) = 8.21. After accounting for hours, residual τ² is 0.0255 and residual I² is 52.3%: hours explain 55.4% of the between-study variance, and the rest is heterogeneity no moderator in the model accounts for. Meta-regression is observational across studies: the slope describes how effects differ between programmes, not what would happen if one programme added an hour.
Output tables explained
- Parameter Estimates
- Intercept and one coefficient per covariate or factor dummy, with SE, z or t, significance and interval. Footnotes state the model and τ² method.
- Model Tests and Residual Heterogeneity
- The omnibus moderator test (Wald χ² or F), residual homogeneity Q with df and significance, τ² or the dispersion φ, residual I², H² and, for random effects, R².
Assumptions and notes
- Moderators are measured at the study level and chosen before looking at the results.
- The effect is linear in each continuous moderator on the analysis scale (log scale for ratios).
- Residual true effects are normally distributed with constant variance τ² (random effects).
- Moderators are not collinear; if they are, the panel asks you to remove one.
How the results are validated
On a seven-study reference set with a continuous and a three-level moderator, fixed-effect coefficients, SEs, the moderator test and residual Q match R metafor 5.2.1 rma(mods=) to 1e-8; REML, DL and ML random-effects τ², coefficients and SEs match to 1e-6, and the moderator test, I² and H² to 1e-5; Knapp-Hartung SEs match to 1e-6 and the F test and p to 1e-5. The multiplicative-dispersion model and R² have no separate reference test. Validation evidence
Questions
How many studies do I need?
A common rule is at least ten studies per moderator. The panel only requires more studies than parameters, but with fewer the coefficients are unreliable and the risk of spurious findings is high.
Should I use the Knapp-Hartung adjustment?
It is generally recommended for random-effects meta-regression: tests become t and F tests with residual df and keep closer to the nominal error rate. Truncating the factor at 1 is a more conservative variant.
What does R² mean here?
The proportional reduction in τ² from the intercept-only model to the model with moderators. It can be 0% even when a moderator is significant, and it is imprecise with few studies.
Where do the effect sizes come from?
Meta-regression takes precomputed effects and standard errors. Compute them from your binary or continuous studies first (for ratios, use the log scale), then add the moderator columns.
Related procedures
- Meta-Analysis: Continuous OutcomesMETA CONTINUOUS
- Meta-Analysis: Binary OutcomesMETA BINARY
- Weight Estimation (WLS)WLS
- Linear Mixed ModelsMIXED
- Free SPSS alternative: full coverage list
Run Meta-Regression on your own data
Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.
SPSS is a trademark of IBM Corp. Crosstabs is not affiliated with or endorsed by IBM.