SEM Mediation Analysis Calculator

This calculator estimates mediation models as structural equation models. It can combine the structural paths from a predictor through a mediator to an outcome with measurement models for latent constructs. The result includes the direct, indirect, and total effects together with the fit and parameter estimates for the complete SEM.

How to calculate mediation with SEM

1. Enter your data and select the measured variables used in the model.
2. Create latent factors and connect their indicators with loading arrows, if required.
3. Draw regression paths from X to M and from M to Y.
4. Add the direct X to Y path if you want to estimate direct and total effects.
5. Select Indirect effect, click the variable where the effect starts, and then click the variable where it ends.
6. Choose delta-method or bootstrap confidence intervals and select Run model.

The indirect-effect action labels the regression paths and defines their product. For a simple mediation model, the indirect effect is the product of the X to M path and the M to Y path. When several connecting chains exist, the calculator can report the separate indirect effects and their sum. A total effect is added when the model also contains a direct path.

Bootstrap confidence intervals

Indirect effects are products of coefficients and their sampling distributions are often asymmetric. The bootstrap option refits the model to 1,000 resampled datasets and reports percentile confidence intervals. It takes longer than the delta method because the entire model is repeatedly estimated in the browser. Initial model results appear before the bootstrap calculation has finished, and the calculation can be cancelled.

How to interpret the mediation results

The indirect effect estimates how much of the relationship between X and Y follows the specified path through M. The direct effect is the X to Y path while M is included in the model. The total effect combines the direct effect with the modeled indirect effects. Confidence intervals describe the uncertainty of these estimates. Statistical evidence for an indirect effect does not by itself establish causality; causal interpretation depends on the design, timing, assumptions, and absence of relevant confounding.

Latent-variable and measured-variable mediation

Use this SEM calculator when one or more constructs are latent, when several indirect paths must be estimated in one model, or when you need global SEM fit measures. If X, M, and Y are three measured variables and you only need a standard regression-based mediation analysis, use the moderator and mediator calculator. For a path model containing measured variables but no factors, see the path analysis calculator.