Empirical Comparison of Factor and Order Analysis on Prestructured and Random Data.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Factor analytic models are widely used for dimensionality assessment.
• Inferential models of order analysis offer an alternative approach to analyzing data structures.

Purpose of the Study:

• To empirically compare the performance of an inferential model of order analysis against traditional factor analytic models.
• To evaluate the models' ability to identify true dimensionality versus spurious patterns in data.

Main Methods:

• Comparative analysis of two distinct datasets: a prestructured dataset (Thurstone's box data) and a random dataset (replication of the Armstrong and Soelberg study).
• Application of both inferential order analysis and factor analytic models to each dataset.

Main Results:

• Both order analysis and factor analytic models successfully identified the true dimensions (length, width, height) in the prestructured dataset.
• Factor analytic models erroneously indicated the presence of dimensionality in the random dataset, where no true structure existed.

Conclusions:

• Factor analytic models may be prone to identifying false dimensionality in unstructured or random data.
• Inferential order analysis demonstrates potential as a robust method for dimensionality assessment, particularly in avoiding spurious findings.