The Unified Model Graph: Drawing the Statistical Models of Psychology

Abstract

Psychologists describe their statistical models with diagrams. The conventions in use, path diagrams, multilevel panels, plate notation, and causal graphs, each grew inside one modeling tradition, and they disagree on basic symbols. As a result, one figure can stand for two different models. An ellipse with three arrows can show a factor model or a latent profile model. A labeled arrow can show a fixed slope or a person-varying slope. A mediation triangle can show a regression decomposition or a causal claim. This article introduces the Unified Model Graph (UMG), a notation built so that the figure identifies the model that was fitted. Three visual cues type every quantity: fill for observed versus latent, shape for continuous versus categorical, and outline for inferential role. Four edge types separate regression, covariance, deterministic, and mixture relations. Plates mark replication, and a badge states whether the figure makes a causal claim. Every well-formed UMG corresponds to exactly one family of distributions, and path diagrams, plate notation, and causal graphs are special cases; the formal results and proofs are in the supplemental material. The accompanying R package \pkg{} builds diagrams from code or from fitted lavaan, lme4, mirt, and brms objects, validates them, translates them to and from lavaan syntax, checks necessary identification conditions, derives testable implications, and generates model-implied data displays. A benchmark of eight R diagramming packages on ten representational features and ten operations locates what the notation adds. All materials, scripts, and outputs are openly archived.

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BibTeX RIS

BibTeX

@misc{yu2026unified,
  title = {{The Unified Model Graph: Drawing the Statistical Models of Psychology}},
  author = {Hsiu-Ting Yu},
  howpublished = {PsyArXiv},
  year = {2026},
  month = sep,
  doi = {10.31234/osf.io/mdr9n_v1},
  url = {https://osf.io/preprints/psyarxiv/mdr9n_v1/},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - The Unified Model Graph: Drawing the Statistical Models of Psychology
AU  - Hsiu-Ting Yu
PY  - 2026
DA  - 2026/09/16
PB  - PsyArXiv
DO  - 10.31234/osf.io/mdr9n_v1
UR  - https://osf.io/preprints/psyarxiv/mdr9n_v1/
AB  - Psychologists describe their statistical models with diagrams. The conventions in use, path diagrams, multilevel panels, plate notation, and causal graphs, each grew inside one modeling tradition, and they disagree on basic symbols. As a result, one figure can stand for two different models. An ellipse with three arrows can show a factor model or a latent profile model. A labeled arrow can show a fixed slope or a person-varying slope. A mediation triangle can show a regression decomposition or a causal claim. This article introduces the Unified Model Graph (UMG), a notation built so that the figure identifies the model that was fitted. Three visual cues type every quantity: fill for observed versus latent, shape for continuous versus categorical, and outline for inferential role. Four edge types separate regression, covariance, deterministic, and mixture relations. Plates mark replication, and a badge states whether the figure makes a causal claim. Every well-formed UMG corresponds to exactly one family of distributions, and path diagrams, plate notation, and causal graphs are special cases; the formal results and proofs are in the supplemental material. The accompanying R package \pkg{} builds diagrams from code or from fitted lavaan, lme4, mirt, and brms objects, validates them, translates them to and from lavaan syntax, checks necessary identification conditions, derives testable implications, and generates model-implied data displays. A benchmark of eight R diagramming packages on ten representational features and ten operations locates what the notation adds. All materials, scripts, and outputs are openly archived.
ER  -

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