A Comparative Study of Approximation Methods for Maximum Likelihood Estimation in Generalized Linear Mixed Models (GLMM)

被引：8

作者：

Handayani, Dian ^{[1
,2
]}

Notodiputro, Khairil Anwar ^{[2
]}

Sadik, Kusman ^{[2
]}

Kurnia, Anang ^{[2
]}

机构：

[1] State Univ Jakarta, Dept Math, Jakarta, Indonesia

[2] Bogor Agr Univ, Dept Stat, Bogor, Indonesia

来源：

STATISTICS AND ITS APPLICATIONS | 2017年 / 1827卷

关键词：

Adaptive Gaussian Quadrature; Generalized Linear Mixed Model; Laplace Approximation; Mean Square Error; Penalized Quasi Likelihood; Relative Bias; INFERENCE;

D O I：

10.1063/1.4979449

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

Maximum likelihood estimates in GLMM are often difficult to be obtained since the calculation involves high dimensional integrals. It is not easy to find analytical solutions for the integral so that the approximation approach is needed. In this paper, we discuss several approximation methods to solve high dimension integrals including the Laplace, Penalized Quasi likelihood (PQL) and Adaptive Gaussian Quadrature (AGQ) approximations. The performance of these methods was evaluated through simulation studies. The 'true' parameter in the simulation was set to be similar with parameter estimates obtained by analyzing a real data, particularly salamander data (McCullagh & Nelder, 1989). The simulation results showed that the Laplace approximation produced better estimates when compared to PQL and AGQ approximations in terms of their relative biases and mean square errors.

引用

页数：9

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