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

arXiv: https://arxiv.org/abs/2608.19282 · HTML: https://mlsanity.com/paper/2608.19282/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2026.

## Abstract (arXiv)

When factor scores replace true latent scores in nonlinear prediction, measurement error attenuates the recoverable variance of any kth-order component of the regression function by ρk -- the kth 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.