The Extra-Factor Phenomenon Revisited: Unidimensional Unfolding as Quadratic Factor Analysis
Why this work is in the frame
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Bibliographic record
Abstract
The application of linear factor analysis to a set of unfoldable (unidimensional) items produces a two-dimensional solution, called the extra-factor phenomenon, which potentially results in incorrect conclusions about the nature of a set of items (van Schuur& Kiers, 1994). Many explanations have been offered for this phenomenon. This study attempted further clarification within the general theory of factor analysis. Specifically, it was demonstrated that the extra-factor phenomenon arises because: (1) the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model; and (2) at the level of covariance structure, the unidimensional quadratic factor model is not distinguishable from the two-dimensional linear factor model (McDonald, 1967). Also discussed are a number of theoretical linkages and bases of distinguishability that exist between unidimensional unfolding and linear factor analysis.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it