Shedden Kerby, Zucker Robert A
Department of Statistics University of Michigan.
Psychometrika. 2008 Dec;73(4):625-646. doi: 10.1007/s11336-008-9077-9.
Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse.
有限混合模型在生长轨迹数据分析中被广泛应用，以发现随时间表现出相似行为模式的个体亚组。在实际应用中，轨迹通常被建模为多项式，这可能无法捕捉纵向模式的重要特征。针对二分响应测量，我们提出一种用于参数估计的似然惩罚方法，该方法能够比最大似然估计更精确地捕捉各种非线性类均值轨迹形状。我们展示了如何针对此类模型进行轨迹是否随时间不变、线性时变或非线性时变的参数估计和推断。为了说明该方法，我们使用了模拟研究以及来自对药物滥用高危儿童的长期纵向研究的数据。
