Pratt's importance measures in factor analysis : a new technique for interpreting oblique factor models
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Bibliographic record
Abstract
This dissertation introduces a new method, Pratt's measure matrix, for interpreting multidimensional oblique factor models in both exploratory and confirmatory contexts. Overall, my thesis, supported by empirical evidence, refutes the currently recommended and practiced methods for understanding an oblique factor model; that is, interpreting the pattern matrix or structure matrix alone or juxtaposing both without integrating the information. Chapter Two reviews the complexities of interpreting a multidimensional factor solution due to factor correlation (i.e., obliquity). Three major complexities highlighted are (1) the inconsistency between the pattern and structure coefficients, (2) the distortion of additive properties, and (3) the inappropriateness of the traditional cut-off rules as being "meaningful". Chapter Three provides the theoretical rationale for adapting Pratt's importance measures from their use in multiple regression to that of factor analysis. The new method is demonstrated and tested with both continuous and categorical data in exploratory factor analysis. The results show that Pratt's measures are applicable to factor analysis and are able to resolve three interpretational complexities arising from factor obliquity. In the context of confirmatory factor analysis, Chapter Four warns researchers that a structure coefficient could be entirely spurious due to factor obliquity as well as zero constraint on its corresponding pattern coefficient. Interpreting such structure coefficients as Graham et al. (2003) suggested can be problematic. The mathematically more justified method is to transform the pattern and structure coefficients into Pratt's measures. The last chapter describes eight novel contributions in this dissertation. The new method is the first attempt ever at ordering the importance of latent variables for multivariate data. It is also the first attempt at demonstrating and explicating the existence, mechanism, and implications of the suppression effect in factor analyses. Specifically, the new method resolves the three interpretational problems due to factor obliquity, assists in identifying a better-fitting exploratory factor model, proves that a structure coefficient in a confirmatory factor analysis with a zero pattern constraint is entirely spurious, avoids the debate over the choice of oblique and orthogonal factor rotation, and last but not least, provides a tool for consolidating the role off actors as the underlying causes.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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