Detail: Generalized SEM Estimator

The Generalized SEM Estimator fits a Generalized SEM Parametric Model, allowing for non-Gaussian outcomes (such as binary or count variables) and a variety of link functions (e.g., logistic, probit, log link). It extends the classical SEM framework to a broader family of response types.

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

Generalized SEM Estimator

Generalized SEM Estimator

Purpose

  • Estimate structural relations in models where:

    • Some variables are binary, ordinal, or counts.

    • Different nodes may use different link functions and distributions.

  • Provide parameter estimates and fit measures appropriate for generalized linear/SEM-type models.

Inputs and requirements

  • Parametric Model: A Generalized SEM PM specifying:

    • Which variables are treated with which distribution/link (e.g., logistic for binary, Poisson for counts).

    • Structural relations between variables (regressions, latent variables, etc.).

  • Data:

    • Variables conforming to the specified distributions.

    • Sufficient variation across categories and ranges.

  • Estimation options (when available), such as:

    • Choice of link functions (if configurable).

    • Optimization method and convergence tolerance.

    • Handling of missing data.

    • Maximum number of iterations.

How it works (conceptually)

The estimator typically:

  1. For each endogenous variable, sets up a generalized linear model (GLM) or related component consistent with the generalized SEM specification.

  2. Uses iterative procedures (e.g., iteratively reweighted least squares or other gradient-based methods) to jointly estimate parameters across the system, respecting cross-equation constraints and latent structure, if present.

  3. Computes:

    • Parameter estimates,

    • Standard errors (if available),

    • Overall or per-component fit statistics.

Output

  • Parameter estimates:

    • Regression coefficients on the scale of the chosen link function.

    • Variance components or dispersion parameters, when applicable.

  • Fit information, which may include:

    • Log-likelihood,

    • Information criteria (AIC, BIC),

    • Convergence diagnostics.

  • The fitted model can be stored as an Instantiated Model (Generalized SEM).

Tips and common issues

  • Ensure that the variable coding (e.g., 0/1 for binary) matches the distribution and link choices.

  • Check convergence diagnostics; generalized SEMs can be more numerically demanding than standard SEMs.

  • If estimation fails or yields extreme parameter values:

    • Inspect for separation in binary outcomes or very low counts.

    • Consider simplifying the model or changing link functions.

    • Verify that the data support the specified distributional assumptions.