Despite broad applications of growth curve models, few studies have dealt with a practical issue – nonnormality of data. Previous studies have used Student’s t distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which intraindividual measurement errors follow unknown random distributions with Dirichlet process mixture priors. Based on Monte Carlo simulations, we evaluate the performance of the robust semiparametric Bayesian method and compare it to the robust method using Student’s t distributions as well as the traditional normal-based method. We conclude that the semiparametric Bayesian method is more robust against nonnormal data. An example about the development of mathematical abilities is provided to illustrate the application of robust growth curve modeling, using school children’s Peabody Individual Achievement Test mathematical test scores from the National Longitudinal Survey of Youth 1997 Cohort.

中文翻译：

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增长曲线建模中的稳健贝叶斯方法：使用学生 t 分布与半参数方法

尽管增长曲线模型应用广泛，但很少有研究涉及实际问题——数据的非正态性。以前的研究使用学生的 t 分布来解决非正态问题。在这项研究中，从半参数贝叶斯角度提出了稳健的分布增长曲线模型，其中个体内测量误差遵循具有狄利克雷过程混合先验的未知随机分布。基于蒙特卡罗模拟，我们评估了稳健半参数贝叶斯方法的性能，并将其与使用学生 t 分布的稳健方法以及传统的基于正态的方法进行了比较。我们得出结论，半参数贝叶斯方法对非正态数据更稳健。