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The Houdini Transformation: True, but Illusory.

Peter M Bentler¹, Peter C M Molenaar

¹University of California, Los Angeles.

Multivariate Behavioral Research

|November 28, 2012

Summary

The Houdini transformation, intended to remove latent variables, is illusory. Algebraic verification shows that transformed models still contain latent variables, challenging common assumptions in statistical modeling.

Area of Science:

Psychometrics
Statistical Modeling
Structural Equation Modeling

Background:

Molenaar's (2003, 2011) work demonstrated transforming common factor models into factor-free models using the Houdini transformation.
This transformation utilized time series and state space theory concepts.
The prior understanding suggested this transformation could eliminate latent variables.

Purpose of the Study:

To algebraically verify the Houdini transformation on a general latent variable model.
To investigate the nature of the transformed model and its latent variable status.
To address the common misconception regarding the factor-free nature of the transformed model.

Main Methods:

Algebraic verification of the Houdini transformation.

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Analysis of a general latent variable model.

Theoretical examination of model equivalence and latent variable presence.

Main Results:

The Houdini transformation was found to be illusory.
The transformed model demonstrably remains a latent variable model.
Path models with only observed variables and residual errors can be latent variable models.

Conclusions:

The Houdini transformation does not eliminate latent variables.
The perceived factor-free nature of the transformed model is a misconception.
This finding necessitates a re-evaluation of models presented as purely observational.