Helwig Nathaniel E
Department of Psychology, University of Minnesota, 75 E River Road, Minneapolis, MN 55455, USA.
School of Statistics, University of Minnesota, 224 Church Street SE, Minneapolis, MN 55455, USA.
Biom J. 2017 Jul;59(4):783-803. doi: 10.1002/bimj.201600045. Epub 2016 Dec 26.
Longitudinal data are inherently multimode in the sense that such data are often collected across multiple modes of variation, for example, time × variables × subjects. In many longitudinal studies, multiple variables are collected to measure some latent construct(s) of interest. In such cases, the goal is to understand temporal trends in the latent variables, as well as individual differences in the trends. Multimode component analysis models provide a powerful framework for discovering latent trends in longitudinal data. However, classic implementations of multimode models do not take into consideration functional information (i.e., the temporal sequence of the collected data) or structural information (i.e., which variables load onto which latent factors) about the study design. In this paper, we reveal how functional and structural constraints can be imposed in multimode models (Parafac and Parafac2) in order to elucidate trends in longitudinal data. As a motivating example, we consider a longitudinal study on per capita alcohol consumption trends conducted from 1970 to 2013 by the U.S. National Institute on Alcohol Abuse and Alcoholism. We demonstrate how functional and structural information about the study design can be incorporated into the Parafac and Parafac2 alternating least squares algorithms to understand temporal and regional trends in three latent constructs: beer consumption, spirits consumption, and wine consumption. Our results reveal that Americans consume more than the recommended amount of alcohol, and total alcohol consumption trends show no signs of decreasing in the last decade.
纵向数据本质上是多模式的，因为此类数据通常是跨多种变异模式收集的，例如，时间×变量×受试者。在许多纵向研究中，会收集多个变量来测量某些感兴趣的潜在结构。在这种情况下，目标是了解潜在变量的时间趋势以及趋势中的个体差异。多模式成分分析模型为发现纵向数据中的潜在趋势提供了一个强大的框架。然而，多模式模型的经典实现没有考虑关于研究设计的功能信息（即所收集数据的时间序列）或结构信息（即哪些变量加载到哪些潜在因子上）。在本文中，我们揭示了如何在多模式模型（平行因子分析和二阶平行因子分析）中施加功能和结构约束，以阐明纵向数据中的趋势。作为一个激励性的例子，我们考虑美国国立酒精滥用与酒精中毒研究所于1970年至2013年进行的一项关于人均酒精消费趋势的纵向研究。我们展示了如何将关于研究设计的功能和结构信息纳入平行因子分析和二阶平行因子分析交替最小二乘算法，以了解三种潜在结构（啤酒消费、烈性酒消费和葡萄酒消费）的时间和区域趋势。我们的结果表明，美国人饮酒量超过推荐量，并且在过去十年中总酒精消费趋势没有下降的迹象。
