Reply to Comments.

Area of Science:

• Causal inference
• Statistical modeling
• Philosophy of science

Background:

• Structural Equation Modeling (SEM) has shifted from clear causal semantics to an algebraic interpretation.
• This algebraic interpretation, while useful for estimation, is limited in distinguishing competing causal claims.
• Critics often conflate the semantics of causal SEM with the epistemological links between data, knowledge, and causal structure.

Purpose of the Study:

• To elaborate on the distinction between causal SEM semantics and epistemological connections.
• To address critiques of SEM by clarifying this distinction.
• To defend core assumptions of causal SEM, specifically Causal Independence and Faithfulness.

Main Methods:

• Conceptual analysis of causal semantics and epistemology in SEM.
• Defense of Causal Independence and Faithfulness assumptions.
• Discussion of specific challenges raised by commentators.

Main Results:

• The distinction between causal semantics and epistemological connections is crucial for valid causal claims.
• Modern critiques of SEM often arise from conflating these two aspects.
• The Causal Independence and Faithfulness assumptions are defended against significant challenges.

Conclusions:

• Clarifying the semantics-epistemology distinction strengthens causal inference with SEM.
• Defending key assumptions is vital for the robust application of SEM in scientific research.
• Addressing commentator concerns refines the understanding and application of causal SEM.