Nummi Tapio, Möttönen Jyrki, Väkeväinen Pasi, Salonen Janne, O'Brien Timothy E
Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland.
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.
J Appl Stat. 2025 Feb 7;52(12):2271-2290. doi: 10.1080/02664763.2025.2459293. eCollection 2025.
When analyzing real data sets, statisticians often face the question that the data are heterogeneous and it may not necessarily be possible to model this heterogeneity directly. One natural option in this case is to use the methods based on finite mixtures. The key question in these techniques often is what is the best number of mixtures or, depending on the focus of the analysis, the best number of sub-populations when the model is otherwise fixed. Moreover, when the distribution of the response variable deviates from meeting the assumptions, it's common to employ an appropriate transformation to align the distribution with the model's requirements. To solve the problem in the mixture regression context we propose a technique based on the scaled Box-Cox transformation for normal mixtures. The specific focus here is on mixture regression for longitudinal data, the so-called trajectory analysis. We present interesting practical results as well as simulation experiments to demonstrate that our method yields reasonable results. Associated R-programs are also provided.
在分析实际数据集时，统计学家常常面临这样一个问题：数据是异质的，直接对这种异质性进行建模不一定可行。在这种情况下，一个自然的选择是使用基于有限混合的方法。这些技术中的关键问题通常是，当模型的其他部分固定时，最佳的混合数量是多少，或者根据分析重点，最佳的子群体数量是多少。此外，当响应变量的分布不符合假设时，通常会采用适当的变换来使分布与模型要求一致。为了解决混合回归背景下的这个问题，我们提出了一种基于正态混合的缩放Box-Cox变换的技术。这里的具体重点是纵向数据的混合回归，即所谓的轨迹分析。我们展示了有趣的实际结果以及模拟实验，以证明我们的方法能产生合理的结果。还提供了相关的R程序。
