提出新型神经网络模型，有效分析具有层级结构的纵向数据。
Deep Generalised Mixed Models: a Novel Neural Network Structure for Analysing Hierarchical Data
- 构建可扩展的深层混合效应模型，融合固定与随机效应
- 在缺失数据为随机情况下仍能提供有效推断，支持高维数据
- 适合心理学、教育学等领域的纵向数据分析，尤其处理不完整数据
体验抽样法（ESM）是一种纵向研究设计，要求参与者多次报告其思想、情绪状态和行为。本研究基于“GrowIt!”应用收集的数据，旨在探究疫情期间青少年的日常情绪。现有分析方法面临诸多挑战：传统统计方法难以应对高维数据，而机器学习方法因缺失数据导致的选择偏差可能产生偏倚结果。在该数据集中，曾有强烈负面情绪的青少年更易退出，形成缺失值为“随机缺失”（missing-at-random）的情形，标准机器学习无法处理。为此，本文提出一种新型神经网络架构——深度广义混合模型（Deep Generalised Mixed Models），将混合效应模型推广至深度学习领域，实现对数据均值和相关结构的半参数灵活建模。通过变分自编码器的改进版本及贝叶斯数据增补算法进行估计。该模型可处理任意分布的纵向结果，适应高维设置，并在缺失数据为随机时仍提供有效推断。我们将其应用于GrowIt!研究和多种模拟场景，结果显示模型具备潜力，但存在一定的不稳定性。
原文摘要 · Abstract (English)
The experience sampling method (ESM) is a longitudinal research design where participants report their thoughts, emotional states and behaviours multiple times a day. Our work is motivated by such data collected by the GrowIt! app, which was released to investigate daily emotions among adolescents during the COVID-19 pandemic. Current procedures to analyse ESM data face various challenges. While standard statistical techniques may not scale well to a high-dimensional setting, machine learning procedures can give biased results due to selection bias introduced by missingness. In our motivating dataset, adolescents dropped out due to previous strong feelings of negative emotions. Hence, the implied missing data are of the missing-at-random type that standard machine learning procedures cannot accommodate. We develop a novel neural network architecture that generalises mixed effects models to deep learning to overcome these challenges. It allows semi-parametric and flexible modelling of data's mean and correlation structure through fixed and random effects. For estimation, we use an adaptation of variational auto-encoders and a Bayesian data augmentation algorithm. Through this approach, the model can accommodate longitudinal outcomes following generic distributions, scale well to high-dimensional settings and provide valid inference when data are missing-at-random. We applied the Deep Generalised Mixed Model to the GrowIt! study and various simulations. The results show potential for the Deep Generalised Mixed Model, yet suboptimal performance due to model instability.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。