The general multivariate analysis of variance model has been extensively studied in the statistical literature and successfully applied in many different fields for analyzing longitudinal data. In this article, we consider the extension of this model having two sets of regressors constituting a growth curve portion and a multivariate analysis of variance portion, respectively. Nowadays, the data collected in empirical studies have relatively complex structures though often demanding a parsimonious modeling. This can be achieved for example through imposing rank constraints on the regression coefficient matrices. The reduced rank regression structure also provides a theoretical interpretation in terms of latent variables. We derive likelihood based estimators for the mean parameters and covariance matrix in this type of models. A numerical example is provided to illustrate the obtained results.

中文翻译：

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关于某些降阶扩展增长曲线模型的估计

在统计文献中已经广泛研究了方差模型的一般多变量分析，并成功地将其应用于许多不同领域来分析纵向数据。在本文中，我们考虑该模型的扩展，该模型具有分别构成增长曲线部分和方差部分的多元分析的两组回归变量。如今，尽管经常需要简化模型，但实证研究中收集的数据具有相对复杂的结构。例如，这可以通过在回归系数矩阵上施加秩约束来实现。降阶回归结构还提供了潜在变量方面的理论解释。我们推导了这类模型中均值参数和协方差矩阵的基于似然估计。