Extended Tetrad Analysis in Factor Modelling: Separability and Uncertainty from Multidimensional Dependence Structures Article Swipe
Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of factor models via two subspaces spanned by paired matrices, where determinantal expressions explicitly quantify the contributions of different dimension subsets to the factor structure. This formulation refines rank-based conditions relevant to understanding factor score indeterminacy and the implications of non-uniqueness in instrumental variable estimation for over-identified models. By weighting these multidimensional contributions to encode sensitivity to their variation, we extend the definition of tetrads into an algebraic procedure that establishes conditions for identifying variability components attributable to individual dimensions. Focusing on cases where one factor encodes structural information, we derive minimal conditions-expressed through graph planarity-that ensure such dimension-specific identifiability. The proofs yield both formal verification tools and constructive methods for generating counterexamples where these conditions fail. These counterexamples reveal a type of ambiguity, termed contextuality, in which the comparison of dimensional contributions depends on the choice of remaining reference dimensions, violating well-established axioms of order-theoretic consistency. We relate these findings to specific forms of uncertainty examined in the psychometric literature.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2204.01169
- https://arxiv.org/pdf/2204.01169
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4226192961
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4226192961Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2204.01169Digital Object Identifier
- Title
-
Extended Tetrad Analysis in Factor Modelling: Separability and Uncertainty from Multidimensional Dependence StructuresWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-04-03Full publication date if available
- Authors
-
Mario AngelelliList of authors in order
- Landing page
-
https://arxiv.org/abs/2204.01169Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2204.01169Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2204.01169Direct OA link when available
- Concepts
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Identifiability, Monomial, Mathematics, Counterexample, Observability, Binomial (polynomial), Matrix (chemical analysis), Algebraic number, Unobservable, Pure mathematics, Discrete mathematics, Applied mathematics, Mathematical analysis, Statistics, Materials science, Econometrics, Composite materialTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.dimensions, | 168 |
| abstract_inverted_index.dimensions. | 107 |
| abstract_inverted_index.establishes | 98 |
| abstract_inverted_index.expressions | 40 |
| abstract_inverted_index.formulation | 54 |
| abstract_inverted_index.identifying | 101 |
| abstract_inverted_index.literature. | 188 |
| abstract_inverted_index.sensitivity | 83 |
| abstract_inverted_index.structuring | 7 |
| abstract_inverted_index.uncertainty | 17, 183 |
| abstract_inverted_index.variability | 102 |
| abstract_inverted_index.attributable | 104 |
| abstract_inverted_index.consistency. | 174 |
| abstract_inverted_index.constructive | 136 |
| abstract_inverted_index.implications | 66 |
| abstract_inverted_index.information, | 116 |
| abstract_inverted_index.instrumental | 70 |
| abstract_inverted_index.psychometric | 187 |
| abstract_inverted_index.verification | 133 |
| abstract_inverted_index.contributions | 44, 80, 160 |
| abstract_inverted_index.determinantal | 39 |
| abstract_inverted_index.indeterminacy | 63 |
| abstract_inverted_index.understanding | 60 |
| abstract_inverted_index.contextuality, | 153 |
| abstract_inverted_index.non-uniqueness | 68 |
| abstract_inverted_index.planarity-that | 123 |
| abstract_inverted_index.representation | 27 |
| abstract_inverted_index.counterexamples | 140, 146 |
| abstract_inverted_index.order-theoretic | 173 |
| abstract_inverted_index.over-identified | 74 |
| abstract_inverted_index.representations | 1 |
| abstract_inverted_index.identifiability. | 127 |
| abstract_inverted_index.multidimensional | 79 |
| abstract_inverted_index.well-established | 170 |
| abstract_inverted_index.characterisation. | 21 |
| abstract_inverted_index.dimension-specific | 126 |
| abstract_inverted_index.conditions-expressed | 120 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5011088707 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/10 |
| sustainable_development_goals[0].score | 0.5299999713897705 |
| sustainable_development_goals[0].display_name | Reduced inequalities |
| citation_normalized_percentile |