Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution
Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution
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DOI：
10.1016/j.jmva.2018.02.008
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Sayantee Jana;N. Balakrishnan;J. Hamid
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文献类型：
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作者：
Sayantee Jana;N. Balakrishnan;J. Hamid
增长曲线模型（GCM）假设每个组的曲线形状相同，其中假设组均值由相同次数的多项式表示。因此，该模型是不合适的，当分析数据的研究，涉及组的平均增长曲线表示不同的形状。我们考虑扩展的增长曲线模型（EGCM），这是一个模型，允许组的手段，随着时间的推移遵循不同程度的多项式。现有的推断EGCM假设多变量正态误差，并产生估计，是不是最佳的，当使用在偏态分布的数据分析。在本文中，我们认为多元偏正态（MSN）分布作为EGCM的基本分布，并提供其均值和协方差参数的估计。我们采用了限制期望最大化（REM）算法，这是基于多变量牛顿-拉夫逊（NR）方法和拉格朗日优化。然而，多元NR方法和现有的REM算法仅适用于向量参数，并且本研究中感兴趣的参数是矩阵。因此，我们将NR方法扩展到矩阵参数，从而使我们能够将REM算法扩展到矩阵估计。使用广泛的模拟和真实的数据的例子也被认为是说明我们提出的估计器的应用所提出的估计器的性能进行了检查。
The Growth Curve Model (GCM) assumes the same shape of profiles for each group, where group means are assumed to be represented by polynomials of the same degree. The model, therefore, is inappropriate when analyzing data from studies involving groups with mean growth curves represented by different shapes. We consider the Extended Growth Curve Model (EGCM), which is a model that allows the group means to follow different degrees of polynomials over time. Existing inference on EGCM assumes multivariate normal errors and produces estimators that are not optimal, when used in the analysis of data with skewed distributions. In this paper, we consider the multivariate skew normal (MSN) distribution as the underlying distribution for the EGCM and provide estimators for its mean and covariance parameters. We adopted the Restricted Expectation–Maximization (REM) algorithm, which is based on the multivariate Newton–Raphson (NR) method and Lagrangian optimization. However, the multivariate NR method and the existing REM algorithm are only applicable to vector parameters and the parameters of interest in this study are matrices. We, therefore, extended the NR approach to matrix parameters, that consequently allowed us to extend the REM algorithm to matrix estimators. The performance of the proposed estimators was examined using extensive simulations and a real data example was also considered to illustrate the application of our proposed estimators.