Advancing Statistical Models for Multilevel Research

多层次研究的统计方法仍然是相对较新的，仍有许多有待探索和验证。例如，混合效应位置-尺度（MELS）模型被提出来同时在多个水平上检验均值（位置）和变异性（尺度）相关的假设。然而，MELS模型尚未开发三个或更多层次的分层数据和/或纵向数据。差距的另一个例子是，具有未知随机结点（变点）的增长模型的估计已经集中在单个结点和单个种群上。我的NSERC DG计划的长期目标是阐述几个多层次的方法，并推进多层次研究的统计模型。我的短期目标（SO）是：1）开发具有三层或多层嵌套数据结构的MELS模型; 2）开发用于估计具有不同潜在亚群的多个变点的混合模型; 3）研究参数和非参数模型在多水平潜在类别分析（LCA）中的性能; 4）探索纵向和生存结局联合模型的多水平扩展。对于三水平MELS模型（SO 1），每个水平的均值侧与任何其他混合模型相似，变异性侧是对数线性模型，其中残差方差的对数由每个水平的预测因子的线性函数预测。对于SO2，我们将开始估计具有两个未知节点的三相线性-线性-线性分段增长曲线模型。然后我们将其扩展到非线性增长，并添加混合成分。对于SO 3，我们将开发仿真模型来检查各种多级LCA模型的性能。对于SO 4，我们将建立事件随时间的纵向过程和计数过程的多级联合模型。我的研究团队已经批准了几项多层次研究的数据访问权。这些数据访问将为研究新方法的性能提供独特的机会。我们的高效计算机实验室（包括两台最近购买的Dell PowerEdge机架式服务器）将支持统计计算和模拟。新开发的统计模型将为自然科学和工程研究人员以及政策制定者打开一扇窗口，以新的方式了解他们的数据。我们将通过提供多层次测量和研究设计的指导来促进我们开发的模型的使用。有了这个扩展的工具箱，研究人员可以更好地进行研究，解决世界上关心的问题。新的多层次模型通过应用于实践，将显示统计建模的潜在力量，以产生能够激励实际行动的人和社会的形象。拟议的研究将为HQP提供独特的机会，他们将发展使用统计方法的实用分析和解释技能，以便在自己的专业研究领域取得成功。

The statistical methods for multilevel research are still relatively recent and much remains to be explored and validated. For example, the mixed-effect location-scale (MELS) models were proposed to test mean (location)- and variability (scale)-related hypothesis at multiple levels simultaneously. However, MELS models have not been developed with three or more levels of hierarchical data and/or longitudinal data. Another example of the gap is that the estimation of growth model with unknown random knot (change point) has concentrated on a single knot and a single population. The long-term objective of my NSERC DG program is to elaborate several multilevel methods, and advance statistical models for multilevel research. My short-term objectives (SO) are: 1) To develop the MELS models with three or more levels of nesting data structures; 2) To develop mixture models for estimating the multiple change points with different latent subpopulations; 3) To study performance of parametric and nonparametric models for multilevel Latent Class Analysis (LCA); 4) To explore multilevel extensions of joint models of longitudinal and survival outcomes. For the three-level MELS model (SO1), the mean side at each level is like any other mixed model and the variability side is a log-linear model in which the log of the residual variance is predicted by a linear function of predictors at each level. For SO2, we will start the estimation of three-phase linear-linear-linear piece-wise growth curve model with two unknown knots. Then we will extend it to nonlinear growth and add the mixture components. For SO3, we will develop simulation models to examine the performance of various multilevel LCA models. For SO4, we will develop multilevel joint models of longitudinal process and the counting process of events over time. My research team has granted data access from several multilevel studies. These data access would provide unique opportunities to investigate the performance of new methods. Our high efficiency computer laboratory including two recently purchased Dell PowerEdge Rack Servers will support the statistical computations and simulations. The new developed statistical models will open a window for researchers in natural science and engineering and policy-makers with new ways of understanding their data. We will promote the use of our developed models by providing guidance of multilevel measurement and research design. With this expanded toolbox, researcher can better conduct research that addresses worldly problems of concern. The new multilevel models through application to practice will show the potential power of statistical modeling to produce images of people and society that can motivate practical action. The proposed studies will provide unique opportunities to HQPs, who will develop the practical analytical and interpretive skills of using statistical methods necessary to be successful in their own specialized areas of research.