Changing a Causal Hypothesis without Changing the Fit: some Rules for Generating Equivalent Path Models.

Area of Science:

• Behavioral Sciences
• Statistics
• Causal Inference

Background:

• Linear causal models are increasingly used in behavioral sciences.
• Software like LISREL facilitates the estimation and testing of these models.
• A key challenge is that distinct causal structures can yield equivalent model fits to the same data.

Purpose of the Study:

• To address the issue of model equivalence in causal analysis.
• To define model equivalence as undecidability in principle.
• To present a systematic method for generating equivalent causal models.

Main Methods:

• The study defines model equivalence based on the principle of undecidability.
• Four distinct rules are presented for generating equivalent causal models.
• These rules involve manipulating causal order and residual correlations.

Main Results:

• Rule I and II demonstrate generating equivalent models through causal order inversions.
• Rule III and IV show how to create equivalent models by substituting paths with correlated residuals.
• Three illustrative examples are provided to demonstrate the application of these rules.

Conclusions:

• Understanding model equivalence is crucial for accurate causal interpretation in behavioral research.
• The presented rules offer a practical framework for identifying and generating alternative, equally plausible causal models.
• This work contributes to a more nuanced understanding of causal inference when dealing with complex data structures.