恢复潜变量的非线性函数：合理值神经网络框架
Recovering Nonlinear Functions of Latent Variables: A Plausible-Value Neural Network Framework
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中文总结 AI 辅助
该研究提出PV-ANN框架，通过埃尔米特多项式展开推导边界，在非线性低信度条件下可大幅缩小潜变量非线性函数的恢复差距，且预测准确率未提升，符合理论预期。
中文摘要 AI 辅助
当因子得分在非线性预测中替代真实潜得分时，对于任何线性得分类型，测量误差会使回归函数的任意第k阶分量的可恢复方差衰减ρ^k，其中ρ是得分的决定系数的k次幂。本研究通过埃尔米特多项式展开推导了该边界，并提出PV-ANN（合理值，即保留潜方差的后验抽样，与人工神经网络结合，无需预先指定即可学习函数形式）。该边界适用于潜尺度函数的恢复，而非从观测指标预测结果，对于后者因子得分已足够，因此预计这两个指标会分离。18个条件的模拟支持这两个预测：在非线性低信度条件下，PV-ANN缩小了因子得分学习器与给定真实潜值学习器之间约五分之四的函数形状恢复差距，且随着信度降低差距扩大，而预测准确率未提高，符合理论要求。大五人格应用说明了预期的探索性工作流程，并描绘了弱信号和测量模型误设下的边界条件。
英文摘要
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.
发表机构
- Korea University（高丽大学）
机构由 AI 辅助整理，请以论文原文为准。
