Meta-Analytic Structural Equation Modeling (MASEM)
Combine correlation matrices from published studies and test a structural model on the pooled matrix with two-stage SEM (Cheung and Chan, 2005). Stage 1 pools the correlations with fixed or random effects; stage 2 fits your path model by weighted least squares.
Updated · By Bibin XavierData 14 × 8
| Studytext · 14 levels | Nnumeric | Trust-Valuenumeric | Trust-Satisfactionnumeric | Trust-Loyaltynumeric | Value-Satisfactionnumeric | Value-Loyaltynumeric | Satisfaction-Loyaltynumeric |
|---|---|---|---|---|---|---|---|
| Ahmed (2012) | 389 | 0.34 | 0.533 | 0.457 | 0.396 | 0.334 | 0.625 |
| Brown (2013) | 169 | 0.346 | 0.595 | 0.543 | 0.395 | 0.435 | 0.65 |
| Costa (2014) | 198 | 0.385 | 0.58 | 0.432 | 0.446 | 0.336 | 0.688 |
| Dubois (2015) | 204 | 0.341 | 0.508 | 0.387 | 0.438 | · | 0.568 |
| Eze (2016) | 284 | 0.402 | 0.495 | 0.396 | 0.393 | 0.304 | 0.606 |
| Fischer (2017) | 492 | 0.318 | 0.535 | 0.402 | 0.387 | 0.195 | 0.533 |
| Garcia (2018) | 261 | 0.413 | 0.508 | 0.397 | 0.403 | 0.293 | 0.536 |
| Hassan (2019) | 106 | 0.216 | 0.603 | 0.477 | 0.213 | 0.047 | 0.571 |
Variables and options
VarA-VarB. Leave cells empty or NA when a study did not report a correlation.Results
14 rows · example dataStage 1: pooled correlations
| Pair | k | Total N | Pooled r (GLS) | SE | τ | I² | Q p |
|---|---|---|---|---|---|---|---|
| Trust – Value | 14 | 3,729 | .351 | .0144 | .000 | 0.0% | .616 |
| Trust – Satisfaction | 14 | 3,729 | .530 | .0118 | .000 | 0.0% | .549 |
| Trust – Loyalty | 14 | 3,729 | .424 | .0170 | .037 | 34.9% | .096 |
| Value – Satisfaction | 14 | 3,729 | .401 | .0137 | .000 | 0.0% | .767 |
| Value – Loyalty | 12 | 3,048 | .289 | .0219 | .050 | 42.2% | .060 |
| Satisfaction – Loyalty | 14 | 3,729 | .591 | .0138 | .031 | 37.5% | .077 |
Note. Multivariate GLS pooling (Becker, 1992) with Olkin–Siotani sampling covariances; random effects add the univariate τ² for each correlation. Overall homogeneity test: Q(76) = 82.37, p = .289.
Pooled correlation matrix
| Trust | Value | Satisfaction | Loyalty | |
|---|---|---|---|---|
| Trust | 1 | |||
| Value | .351 | 1 | ||
| Satisfaction | .530 | .401 | 1 | |
| Loyalty | .424 | .289 | .591 | 1 |
Stage 2: model fit
| Index | Value | Threshold | Verdict |
|---|---|---|---|
| χ² / df | — | ≤ 3 (≤ 5 acceptable) | — |
| CFI | 1.000 | ≥ .95 (≥ .90 acceptable) | Good |
| TLI | — | ≥ .95 (≥ .90 acceptable) | Poor |
| RMSEA | — | ≤ .06 (≤ .08 acceptable) | Poor |
| SRMR | .000 | ≤ .08 | Good |
Note. Thresholds follow Hu and Bentler (1999). With small samples or many indicators, judge fit on several indices together.
Structural paths (regressions)
| Path | Label | Estimate | SE | z | p | 95% CI | Standardized (β) |
|---|---|---|---|---|---|---|---|
| Trust → Satisfaction | a | 0.444 | 0.013 | 33.91 | < .001 | [0.418, 0.470] | .444 |
| Value → Satisfaction | 0.245 | 0.014 | 17.47 | < .001 | [0.217, 0.272] | .245 | |
| Satisfaction → Loyalty | b | 0.498 | 0.022 | 23.13 | < .001 | [0.456, 0.540] | .498 |
| Trust → Loyalty | 0.146 | 0.023 | 6.48 | < .001 | [0.102, 0.191] | .146 | |
| Value → Loyalty | 0.038 | 0.025 | 1.55 | .120 | [-0.010, 0.086] | .038 |
Covariances
| Between | Estimate | SE | z | p | Correlation |
|---|---|---|---|---|---|
| Trust ↔ Value | 0.351 | 0.014 | 24.46 | < .001 | .351 |
Explained variance (R²)
| Variable | R² |
|---|---|
| Satisfaction | .333 |
| Loyalty | .367 |
Defined effects (e.g. indirect effects)
| Effect | Definition | Estimate | SE | z | p | 95% CI (delta) | 95% CI (Monte Carlo) |
|---|---|---|---|---|---|---|---|
| indirect | a*b | 0.2210 | 0.0117 | 18.90 | < .001 | [0.198, 0.244] | [0.199, 0.245] |
Note. Monte Carlo confidence intervals (10,000 draws; Preacher and Selig, 2012) do not assume the indirect effect is normally distributed and are preferred for products of coefficients.
Interpretation
Across 14 studies (N = 3,729), the significant standardized paths are Trust → Satisfaction (β = 0.44); Value → Satisfaction (β = 0.24); Satisfaction → Loyalty (β = 0.50); Trust → Loyalty (β = 0.15). The stage 2 model is saturated, so fit is perfect by definition. indirect = 0.221, 95% CI [0.199, 0.245].
How to cite this tool
Using these results in a thesis, journal article, report or class assignment? Please cite this free tool so others can find it. It keeps the site free.
APA 7
Xavier, B. (2026). Meta-Analytic Structural Equation Modeling (MASEM) [Web application]. FreeStatisticalTools.com. https://freestatisticaltools.com/meta-analytic-structural-equation-modeling/
BibTeX
@software{xavier_masem_2026,
author = {Xavier, Bibin},
title = {Meta-Analytic Structural Equation Modeling (MASEM)},
publisher = {FreeStatisticalTools.com},
year = {2026},
url = {https://freestatisticaltools.com/meta-analytic-structural-equation-modeling/},
note = {Web application}
}Suggested sentence for your methods section: “The analysis was carried out with the free Meta-Analytic Structural Equation Modeling (MASEM) tool on FreeStatisticalTools.com (Xavier, 2026).”
What is meta-analytic SEM (MASEM)?
Meta-analytic structural equation modeling combines meta-analysis with SEM. Stage 1 pools the correlation matrices reported by many studies; stage 2 fits a structural model to the pooled matrix, weighting each correlation by its precision, in the two-stage approach of Cheung and Chan (2005).
When to use meta-analytic SEM (MASEM)
Use MASEM to test a theoretical model with evidence from many studies, when no single study measured all relationships, or to assess mediation across a literature.
Assumptions
- Correlations come from independent samples.
- The pooled correlation matrix is positive definite.
- Stage 2 analyses standardized variables, so path coefficients are standardized.
How to set up your data
One row per study with a sample size column and one column per correlation, named VarA-VarB. Missing correlations are allowed.
How to use this tool
- Enter your data. Paste columns from Excel, Google Sheets or SPSS with variable names in the first row, or upload a CSV or Excel file. The example data shows the expected layout.
- Choose the variables. Select the sample size column and stage 2 model (variable names as in the column headers).
- Set the options. Fill in stage 1 pooling.
- Read the results. Results update automatically. Read the plain-English interpretation, then use Copy table to paste APA-style tables into Word and Copy for the results sentence.
How to report meta-analytic SEM (MASEM) in APA style
Report stage 1 heterogeneity and the pooled matrix, then stage 2 fit and standardized paths with confidence intervals (Cheung, 2015).
Frequently asked questions
What data do I need for MASEM?
For each study, its sample size and the correlations among the variables in your model. Studies that report only some correlations can still be included.
Fixed or random effects in stage 1?
Random effects allow the true correlations to vary across studies and are usually more realistic; fixed effects assume one common correlation matrix.
Are MASEM path coefficients standardized?
Yes. Stage 2 analyses a correlation matrix, so all coefficients are standardized.
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