Deletion diagnostics for the generalised linear mixed model with independent random effects.
Deletion diagnostics for the generalised linear mixed model with independent random effects.
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DOI：
10.1002/sim.6810
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发表时间：
2016-04-30
影响因子：
2
通讯作者：
Eisen EA
中科院分区：
文献类型：
--
作者：
Ganguli B;Roy SS;Naskar M;Malloy EJ;Eisen EA
广义线性混合模型（GLMM）广泛用于环境数据建模。然而，这些数据很容易受到有影响的观测结果的影响，这可能会扭曲估计的辐射响应曲线，特别是在高暴露区域。用于迭代估计方案的删除诊断通常基于保持某些关键量（诸如信息矩阵）恒定的整个系统的单次迭代来导出删除的估计。在本文中，我们提出了一个近似公式删除估计和库克距离的GLMM，它不假设方差参数的估计不受删除。该程序允许用户计算平均值和方差参数的标准化DFBETA。在某些情况下，例如当使用GLMM作为平滑设备时，方差参数的此类残差本身就很有趣。在一般情况下，该程序会导致删除的平均参数的估计值，这是校正删除方差分量的影响，因为两组参数的估计是相互依赖的。这些残差的概率行为进行了研究，并建议其标准化的模拟为基础的程序。该方法用于识别暴露于二氧化硅的职业队列中有影响力的个人。结果表明，如果不对方差分量进行后模型拟合诊断，可能会导致关于拟合曲线的错误结论和不稳定的置信区间。
The Generalised Linear Mixed Model (GLMM) is widely used for modelling environmental data. However, such data are prone to influential observations which can distort the estimated exposure-response curve particularly in regions of high exposure. Deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant. In this paper, we present an approximate formula for the deleted estimates and Cook’s distance for the GLMM which does not assume that the estimates of variance parameters are unaffected by deletion. The procedure allows the user to calculate standardised DFBETAs for mean as well as variance parameters. In certain cases, such as when using the GLMM as a device for smoothing, such residuals for the variance parameters are interesting in their own right. In general, the procedure leads to deleted estimates of mean parameters which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent. The probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation. The method is used to identify influential individuals in an occupational cohort exposed to silica. The results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals.