Metraipolis › archive › dc_80db67f72ef2

Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework — arXiv:2608.19282

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.19282
License (as archived): CC0-1.0
Archived: 2026-10-18T11:48:33.267Z
SHA-256 of the archived text: bf6de0c504a55b560e00664f2f2405e2a42d148b32a7c8f366fb7f4fc581dfc8
Stable URL of this page: https://metraipolis.com/documento/dc_80db67f72ef2

How to cite

Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework — arXiv:2608.19282 — arXiv (en), https://arxiv.org/abs/2608.19282 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_80db67f72ef2 (Metraipolis archive dc_80db67f72ef2, sha256 bf6de0c504a55b560e00664f2f2405e2a42d148b32a7c8f366fb7f4fc581dfc8)

BibTeX

@misc{dc80db67f72ef2,
  title = {Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework — arXiv:2608.19282},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.19282},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_80db67f72ef2; sha256 bf6de0c504a55b560e00664f2f2405e2a42d148b32a7c8f366fb7f4fc581dfc8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.19282. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

When factor scores replace true latent scores in nonlinear prediction, measurement error attenuates the recoverable variance of any $k$th-order component of the regression function by $\rho^k$ -- the $k$th power of the score's coefficient of determination -- for any linear score type. This study derives the bound via Hermite polynomial expansion and proposes PV-ANN -- plausible values (posterior draws preserving latent variance) combined with artificial neural networks (learning functional form without prespecification). The bound governs recovery of the latent-scale function, not prediction of the outcome from observed indicators, for which factor scores are already sufficient; the two metrics are therefore predicted to dissociate. An 18-condition simulation supports both predictions: in the nonlinear low-reliability conditions PV-ANN closes about four fifths of the function-shape recovery gap between a factor-score learner and one given the true latent values, and the margin widens as reliability falls, while predictive accuracy is not improved, as the theory requires. A Big Five application illustrates the intended exploratory workflow and delineates boundary conditions under weak signal and measurement model misspecification.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-21 in cs.LG).
Categorie arXiv: Methodology (stat.ME) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2608.19282 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T11:47:43.354Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).