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    Area of Science:

    • Statistics
    • Causal Inference
    • Econometrics

    Background:

    • Conventional structural equation modeling (SEM) relies on global covariance structure fitting, which can yield misleading results due to insufficient focus on specific model constraints.
    • Goodness-of-fit tests in traditional SEM do not adequately assess the implied constraints of the model.
    • Directed acyclic graph (DAG) theory offers an alternative for checking identifiability and constraints, but is limited for models with correlated disturbances.

    Purpose of the Study:

    • To present a novel algebraic approach to structural equation modeling that overcomes limitations of DAG theory.
    • To develop a method for equation-by-equation identifiability checking and constraint testing.
    • To provide consistent parameter estimators in closed form for specific structural equation models.

    Main Methods:

    • Utilizes new algebraic results to extend DAG theory for models with correlated disturbances.
    • Implements a specific structural equation analysis that checks identifiability and tests constraints individually.
    • Derives consistent parameter estimators in closed form directly from the equations.

    Main Results:

    • The new method provides a complete approach for Markov models and extends analysis to models with correlated disturbances.
    • Identifiability is checked, and constraints are tested equation by equation.
    • Consistent parameter estimators are obtained in closed form.

    Conclusions:

    • The developed specific structural equation modeling offers a more rigorous alternative to global covariance structure analysis.
    • The method is currently applicable to recursive models with exclusion conditions.
    • Further research may lead to a comprehensive alternative for all structural equation models.