Just finished reading “The Causal Foundations of Structural Equation Modeling” by Judea Pearl, February 2012, UCLA, Technical Report R-370.

This paper has many very useful ideas.
One it highlights and resolves is the symmetry/asymmetry problem or paradox that exists in the fact that the linear model
in statistics has a symmetry between the independent and dependent variables which are then consequently labeled and treated differently.
Dr. Pearl traces the cause back to the equality sign in the linear model.
In one sense it is treated as an assignment equality sign as in computer science and in another sense it is treated as the equality sign in mathematics.
The solution to the paradox is found in the use of structural equation modeling and the treatment of causality.
The methodology requires the specification of causal assumptions, quries of interest and data.
The structural equation methodology results in: logical implications of the assumptions, causal inference, testable implications, statistical inference, model testing (goodness of fit) and conditional claims.
If you ever noticed and were concerned about the symmetry in the linear model and its apparent assymetry in modeling then this is a great paper to read!

I enjoyed Dr. Pearl’s talk at the Joint Statistical meetings and this paper is a great followup to that presentation.

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