用神经网络恢复潜变量非线性关系，解决测量误差导致的函数失真问题。
Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework
- 结合后验抽样与神经网络，构建可学习任意函数形式的潜变量恢复框架
- 在低信度条件下，该方法能恢复约80%的真实函数形状差距
- 适合潜变量非线性建模场景，尤其在信号弱或模型有误设时仍有效
当用因子得分替代真实潜变量进行非线性预测时，测量误差会使回归函数中任意k阶成分的可恢复方差衰减至真实值的ρ^k（ρ为得分决定系数的幂）。本研究通过赫尔米特多项式展开推导出该边界，并提出PV-ANN框架：利用后验抽样（保留潜变量方差）与人工神经网络结合，无需预设函数形式即可学习复杂关系。该边界限制的是潜变量尺度下的函数恢复能力，而非基于观测指标的预测性能——两者理论上应分离。18组条件的模拟验证了两点：在非线性低信度情形下，PV-ANN使因子得分模型与已知真实潜变量模型之间的函数形状恢复差距缩小约四分之五，且随信度下降而扩大；但预测准确率未提升，符合理论预期。对大五人格数据的应用展示了其探索性分析流程，并揭示了在弱信号和测量模型误设下的边界条件。
原文摘要 · Abstract (English)
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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