Detail: SEM (Linear) Estimator

The SEM (Linear) Estimator fits a Structural Equation Model (SEM) Parametric Model to continuous data, assuming linear relations with Gaussian errors. It produces parameter estimates (path coefficients, variances, and possibly means) and global fit statistics.

This estimator is available when the Parametric Model connected to the Estimator box is a SEM PM.

SEM Estimator

SEM Estimator

Purpose

  • Estimate:

    • Regression/path coefficients between variables.

    • Error variances and possibly covariances.

    • Optionally, intercepts/means (depending on model specification).

  • Provide model fit statistics such as:

    • χ², degrees of freedom, and p-value.

    • Additional indices like RMSEA, CFI, TLI, BIC (when available).

Inputs and requirements

  • Parametric Model: A SEM PM specifying:

    • Directed edges (structural equations),

    • (Optional) latent variables and measurement relations.

  • Data:

    • Continuous measurements aligned with observed variables in the SEM.

    • Sufficient sample size and variance structure for identification.

  • Estimation options (when exposed), e.g.:

    • Handling of means (with or without mean structure).

    • Missing-data method (e.g., listwise deletion, FIML).

    • Optimization tolerance and maximum iterations.

    • Robust corrections (if supported).

How it works (conceptually)

The SEM (Linear) Estimator typically:

  1. Constructs an implied covariance (and mean) model from the SEM PM.

  2. Finds parameters that minimize a discrepancy function between:

    • the observed sample covariance (and mean) structure, and

    • the model-implied covariance (and mean) structure.

  3. Uses numerical optimization (e.g., ML-based) to obtain parameter estimates and compute fit statistics.

Output

  • Parameter table showing:

    • Path coefficients (regression weights).

    • Error variances and (where applicable) covariances.

    • Standard errors and test statistics (if available).

  • Fit indices:

    • χ², df, p-value.

    • Additional indices (RMSEA, CFI, TLI, BIC, etc.), depending on the implementation.

  • Convergence information and any warnings (e.g., non-positive definite covariance, Heywood cases).

The result can be stored as an Instantiated Model (SEM) for later use.

File menu options (SEM Estimator)

The File menu of the SEM (Linear) Estimator provides several ways to export or reuse the fitted model and its matrices:

  • Save SEM as XML
    Saves the fitted SEM in Tetrad’s XML format, including the graph structure, estimated parameters, and error (co)variances. This XML can be reloaded into Tetrad as an instantiated SEM or processed by external tools.

  • Copy Implied Covariance Matrix
    Copies the model-implied covariance matrix (\hat\Sigma) of the fitted SEM to the system clipboard as tabular text. You can paste this into a spreadsheet, R, Python, or another program.

  • Copy Coefficient Matrix
    Copies the matrix of regression/path coefficients (the structural coefficient matrix) to the clipboard as tabular text.

  • Copy Error Covariance Matrix
    Copies the residual/error covariance matrix to the clipboard as tabular text.

  • Save Graph Image…
    Saves an image of the SEM graph corresponding to the fitted parametric model. This is useful for including the estimated model in papers, slides, or reports.

  • Save SEM as Lavaan
    Saves the fitted SEM as lavaan model syntax in a .lav file.
    When you choose this option, a dialog lets you select:

    • Whether to include intercepts (Y ~ c*1),

    • Whether to include residual variances (Y ~~ v*Y),

    • Whether to include residual covariances (Y ~~ c*Z),

    • And whether to fix parameters to their current values or export them as lavaan start() values for re-estimation.

    The resulting .lav file can be read directly in R using the lavaan package, for example:

    model <- readLines("sem-im.lav")
fit   <- lavaan::sem(model, data = mydata)