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

• URL: http://arxiv.org/abs/2608.19282v1
• Date: Wed, 19 Aug 2026 08:27:55 GMT
• Title: Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework
• Abstract summary: When factor scores replace true latent scores in nonlinear prediction, measurement error attenuates the recoverable variance by $k$.<n>The bound recovery governs the latent-scale function, not prediction of the outcome from observed indicators.<n>An 18-condition simulation supports both predictions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $ρ^k$ -- 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.

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