Empirical best prediction under area-level Poisson mixed models
Empirical best prediction under area-level Poisson mixed models
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DOI：
10.1007/s11749-015-0469-8
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发表时间：
2016-09-01
期刊：
影响因子：
1.3
通讯作者：
Morales, Domingo
中科院分区：
文献类型：
--
作者：
Boubeta, Miguel;Jose Lombardia, Maria;Morales, Domingo
本文研究了区域级泊松混合模型估计小区域计数指标的适用性。在拟合广义线性模型的可用程序中，采用了矩量法（MM）和惩罚拟似然法（PQL）。使用 MM 导出面积平均值的经验最佳预测因子 (EBP)，并与使用 MM 和 PQL 的插件替代方案进行比较。使用 PQL 的插件估计器计算速度更快，并且相对于涉及高复杂积分的 EBP 提供有竞争力的性能。给出了 EBP 均方误差 (MSE) 的近似值，并提出了三个 MSE 估计器。前两个 MSE 估计器是插件估计器，没有或有二阶偏差校正，第三个基于参数引导。进行了几个模拟实验来分析 EBP 的行为并比较 EBP 的 MSE 估计器。在实践中，引导程序替代方案是一个不错的选择，因为它的性能与分析版本类似，并且计算速度更快。开发的方法和软件适用于 2008 年西班牙生活状况调查的数据。该应用程序的目标是估算省级贫困率。
The paper studies the applicability of area-level Poisson mixed models to estimate small area counting indicators. Among the available procedures for fitting generalized linear models, the method of moments (MM) and the penalised quasi-likelihood (PQL) method are employed. The empirical best predictor (EBP) of the area mean is derived using MM and compared with plug-in alternatives using MM and PQL. The plug-in estimator using PQL is computationally faster and provides competitive performance with respect to EBP that involves high complex integrals. An approximation to the mean squared error (MSE) of the EBP is given and three MSE estimators are proposed. The first two MSE estimators are plug-in estimators without and with bias correction to the second order and the third one is based on parametric bootstrap. Several simulation experiments are carried out for analysing the behaviour of the EBP and for comparing the estimators of the MSE of the EBP. A good choice in practice is the bootstrap alternative since it performs similarly to the analytical versions and is computationally faster. The developed methodology and software are applied to data from the 2008 Spanish living condition survey. The target of the application is the estimation of poverty rates at province level.