EM algorithms for nonlinear mixed effects models
EM algorithms for nonlinear mixed effects models
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DOI：
10.1016/j.csda.2006.11.022
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发表时间：
2007-03-01
影响因子：
1.8
通讯作者：
Wang, Jing
中科院分区：
文献类型：
--
作者：
Wang, Jing
在非线性混合效应模型（NLMM）中，用Monte Carlo EM算法（MCEM）求最大似然估计（MLE）时，由于目标分布的复杂性，在获得用于估计E步的样本时遇到了很大的困难。抽样方法，如马尔可夫链技术和重要性抽样已被用来减轻这种困难。马尔可夫链的优点是它们比基于独立样本的方法适用于更广泛的分布。然而，在许多情况下，马尔可夫链的计算成本是显着大于独立的采样器。基于独立样本的MCEM算法允许直接评估Monte Carlo误差，并且当选择有效的候选分布时，可以比基于马尔可夫链的算法更有效，这形成了本文的动机。本文提出的MCEM算法使用的样本从一个易于模拟和有效的重要性分布，使计算强度和复杂性大大降低。此外，所提出的MCEM算法保留了独立样本在测量Monte Carlo误差时引入的灵活性，从而允许Monte Carlo样本大小随着EM迭代次数的增加而增加。我们还介绍了一个EM算法，使用高斯正交近似（GQEM）的E步骤。在低维情况下，GQEM算法比所提出的MCEM算法更有效，因此可以用作替代方案。使用真实的数据示例和仿真，将所提出的EM方法的性能与现有的ML估计进行比较。(c)2006 Elsevier B.V.保留所有权利。
Implementing the Monte Carlo EM algorithm (MCEM) algorithm for finding maximum likelihood estimates (MLEs) in the nonlinear mixed effects model (NLMM) has encountered a great deal of difficulty in obtaining samples used for estimating the E step due to the intractability of the target distribution. Sampling methods such as Markov chain techniques and importance sampling have been used to alleviate such difficulty. The advantage of Markov chains is that they are applicable to a wider range of distributions than the approaches based on independent samples. However, in many cases the computational cost of Markov chains is significantly greater than that of independent samplers. The MCEM algorithms based on independent samples allow for straightforward assessment of Monte Carlo error and can be considerably more efficient than those based on Markov chains when an efficient candidate distribution is chosen, which forms the motivation of this paper. The proposed MCEM algorithm in this paper uses samples obtained from an easy-to-simulate and efficient importance distribution so that the computational intensity and complexity is much reduced. Moreover, the proposed MCEM algorithm preserves the flexibility introduced by independent samples in gauging Monte Carlo error and thus allows the Monte Carlo sample size to increase with the number of EM iterations. We also introduce an EM algorithm using Gaussian quadrature approximations (GQEM) for the E step. In low-dimensional cases, the GQEM algorithm is more efficient than the proposed MCEM algorithm and thus can be used as an alternative. The performances of the proposed EM methods are compared to the existing ML estimators using real data examples and simulations. (c) 2006 Elsevier B.V. All rights reserved.