Kohli Nidhi, Harring Jeffrey R, Zopluoglu Cengiz
Quantitative Methods in Education Program, Department of Educational Psychology, University of Minnesota, 161 Education Sciences Bldg., 56 East River Road, Minneapolis, MN, 55455 , USA.
University of Maryland, College Park, MD, USA.
Psychometrika. 2016 Sep;81(3):851-80. doi: 10.1007/s11336-015-9462-0. Epub 2015 Apr 30.
Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation-maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data.
连续纵向数据的非线性随机系数模型（NRCMs）常用于研究测量变量随时间呈现非线性发展（或增长）模式的个体行为。作为该模型的扩展，本研究考虑了NRCMs的有限混合模型，它将NRCMs的特征与有限混合（或潜在类别）模型的思想相结合。该模型的功效在于，它允许整合本质上的非线性函数，其中数据来自两个或更多未观察到的亚群体的混合，从而允许同时研究个体内（个体内部）变异性、个体间（个体之间）变异性和亚群体异质性。通过进行蒙特卡罗模拟研究，检验了该模型在实际数据分析条件下的有效性。模拟研究使用专门为本研究目的开发的R程序进行。该R程序使用期望最大化算法的最大似然法。研究设计模仿了在任务完成数据上运行两类混合模型所获得的输出。
