APPROXIMATE INFERENCE IN GENERALIZED LINEAR MIXED MODELS
APPROXIMATE INFERENCE IN GENERALIZED LINEAR MIXED MODELS
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DOI：
10.1080/01621459.1993.10594284
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发表时间：
1993-03-01
影响因子：
3.7
通讯作者：
CLAYTON, DG
中科院分区：
文献类型：
--
作者：
BRESLOW, NE;CLAYTON, DG
过度分散，相关误差，收缩估计和平滑回归关系的统计方法可以包含在广义线性混合模型（GLMM）的框架内。给定随机效应的未观测向量，假设观测值是条件独立的，均值通过指定的链接函数依赖于线性预测值，条件方差由方差函数、已知先验权重和比例因子指定。假设随机效应为正态分布，均值为零，离差矩阵取决于未知方差分量。对于涉及时间序列、空间聚合和平滑的问题，可以根据秩亏逆协方差矩阵来指定离散度。使用拉普拉斯的方法的边际准似然近似最终导致估计方程的基础上惩罚quasilikidity或PQL的平均参数和伪似然的方差。实施涉及到重复调用正常的理论程序的REML估计方差分量的问题。通过非正式的数学论证、模拟和一系列的工作实例，我们得出结论：PQL对于分层模型中参数的近似推断和随机效应的实现具有实用价值。这些应用包括种子发芽二项比例的过度分散：癫痫患者发病率的纵向分析;乳腺癌发病率年龄组模型中出生组群效应的平滑;儿童癌症和产科辐射病例对照研究中出生组群效应曲率的评价;苏格兰各县唇癌发病率的空间聚集;以及蝾螈在一项复杂的实验中成功交配，该实验涉及雄性和雌性效应的交叉。PQL倾向于低估方差分量和（绝对值）固定效应时，应用于集群二进制数据，但这种情况迅速改善二项式观测具有大于1。
Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Implementation involves repeated calls to normal theory procedures for REML estimation in variance components problems. By means of informal mathematical arguments, simulations and a series of worked examples, we conclude that PQL is of practical value for approximate inference on parameters and realizations of random effects in the hierarchical model. The applications cover overdispersion in binomial proportions of seed germination: longitudinal analysis of attack rates in epilepsy patients; smoothing of birth cohort effects in an age-cohort model of breast cancer incidence; evaluation of curvature of birth cohort effects in a case-control study of childhood cancer and obstetric radiation; spatial aggregation of lip cancer rates in Scottish counties; and the success of salamander matings in a complicated experiment involving crossing of male and female effects. PQL tends to underestimate somewhat the variance components and (in absolute value) fixed effects when applied to clustered binary data, but the situation improves rapidly for binomial observations having denominators greater than one.