We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with latent and observed variables depending smoothly on observed variables. A profile likelihood algorithm is proposed, and we derive asymptotic standard errors of both smooth and parametric terms. The work was motivated by applications in cognitive neuroscience, and we show how GALAMMs can successfully model the complex lifespan trajectory of latent episodic memory, along with a discrepant trajectory of working memory, as well as the effect of latent socioeconomic status on hippocampal development. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.
翻译:我们提出了通用添加剂潜伏和混合模型(GALAMMS),用于分析集成数据,根据观察到的变量顺利地分析潜在和观察到的变量。提出了剖析概率算法,并得出了平滑和参数术语的零星标准误差。这项工作的动机是认知神经科学的应用,我们展示了GALAMMS如何成功地模拟潜在偶发记忆的复杂生命周期轨迹,以及工作记忆的不均轨轨迹,以及潜在社会经济地位对河马运动发展的影响。模拟实验表明,模型估计即使有中度样本大小也是准确的。