Department of Psychology, University of Oslo, Oslo, Norway.
Department of Radiology and Nuclear Medicine, Oslo University Hospital, Oslo, Norway.
Psychometrika. 2023 Jun;88(2):456-486. doi: 10.1007/s11336-023-09910-z. Epub 2023 Mar 28.
We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can jointly model the complex lifespan trajectories of episodic memory, working memory, and speed/executive function, measured by the California Verbal Learning Test (CVLT), digit span tests, and Stroop tests, respectively. Next, we study the effect of socioeconomic status on brain structure, using data on education and income together with hippocampal volumes estimated by magnetic resonance imaging. By combining semiparametric estimation with latent variable modeling, GALAMMs allow a more realistic representation of how brain and cognition vary across the lifespan, while simultaneously estimating latent traits from measured items. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.
我们提出了广义可加潜在混合模型（GALAMMs），用于分析具有响应变量和潜在变量的聚类数据，这些变量与观测变量平滑相关。我们提出了一种可扩展的最大似然估计算法，利用拉普拉斯逼近、稀疏矩阵计算和自动微分。混合响应类型、异方差和交叉随机效应自然地融入到框架中。所开发的模型源于认知神经科学中的应用，我们提出了两个案例研究。首先，我们展示了 GALAMMs 如何联合建模加州词语学习测试（CVLT）、数字跨度测试和斯特鲁普测试分别测量的情景记忆、工作记忆和速度/执行功能的复杂寿命轨迹。接下来，我们研究了社会经济地位对大脑结构的影响，使用了教育和收入数据以及通过磁共振成像估计的海马体体积。通过将半参数估计与潜在变量建模相结合，GALAMMs 允许更真实地表示大脑和认知在整个生命周期中的变化，同时从测量项目中估计潜在特征。模拟实验表明，即使在中等样本量的情况下，模型估计也是准确的。
