Residual diagnostics for growth mixture models: Examining the impact of a preventive intervention on multiple trajectories of aggressive behavior
Residual diagnostics for growth mixture models: Examining the impact of a preventive intervention on multiple trajectories of aggressive behavior
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DOI：
10.1198/016214505000000501
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发表时间：
2005-09-01
影响因子：
3.7
通讯作者：
Bandeen-Roche, K
中科院分区：
文献类型：
--
作者：
Wang, CP;Brown, CH;Bandeen-Roche, K
生长混合模型已成为研究种群内发育轨迹异质性的重要工具。在本文中，我们开发了图形诊断来检测生长混合模型中关于生长类数量、生长轨迹均值和协方差结构的错误说明。对于每个模型的错误规范，我们提出了不同类型的经验贝叶斯残差来量化偏离。我们的程序首先是为样本输入多个独立的生长类别集。然后，从这些所谓的“伪类”图中，我们形成诊断图来检查每个此类中残差的平均经验分布。我们的建议利用了这样一种特性，即当底层模型正确时，每一组假类调整残差都是具有已知均值和（co）方差的渐近正态。这些方法在涉及两类线性增长曲线的模拟研究中是合理的，这两类线性增长曲线的协方差结构也不同。然后将这些数据应用于随机现场试验的纵向数据，该试验测试儿童的攻击行为轨迹是否可以在小学和中学期间进行修改。我们的诊断得出了一个混合了三种生长类型的解决方案。通过比较多个伪类的诊断结果和多个输入的诊断结果，我们展示了前者的计算优势，并得到了确定伪类提取的最小数量的准则。
Growth mixture modeling has become a prominent tool for studying the heterogeneity of developmental trajectories within a population. In this article we develop graphical diagnostics to detect misspecification in growth mixture models regarding the number of growth classes, growth trajectory means, and covariance structures. For each model misspecification, we propose a different type of empirical Bayes residual to quantify the departure. Our procedure begins by imputing multiple independent sets of growth classes for the sample. Then, from these so-called "pseudoclass" draws, we form diagnostic plots to examine the averaged empirical distributions of residuals in each such class. Our proposals draw on the property that each single set of pseudoclass adjusted residuals is asymptotically normal with known mean and (co)variance when the underlying model is correct. These methods are justified in simulation studies involving two classes of linear growth curves that also differ by their covariance structures. These are then applied to longitudinal data from a randomized field trial that tests whether children's trajectories of aggressive behavior could be modified during elementary and middle school. Our diagnostics lead to a solution involving a mixture of three growth classes. When comparing the diagnostics obtained from multiple pseudoclasses with those from multiple imputations, we show the computational advantage of the former and obtain a criterion for determining the minimum number of pseudoclass draws.