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

Abstract: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.

51 pages, 4 figures, 24 tables. Data, materials, and code: this https URL

Methodology (stat.ME); Machine Learning (cs.LG)

arXiv:2608.19282 [stat.ME]

(or arXiv:2608.19282v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2608.19282 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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