Consistency Inference Property of QIC in Selecting the True Working Correlation Structure for Generalized Estimating Equations
Consistency Inference Property of QIC in Selecting the True Working Correlation Structure for Generalized Estimating Equations
复制标题
QIC在选择广义估计方程真实工作相关结构中的一致性推理性质
DOI：
10.11648/j.ajtas.20190802.14
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Edgar Ouko Otumba
中科院分区：
文献类型：
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作者：
R. N. Nyabwanga;Fredrick Onyango;Edgar Ouko Otumba
广义估计方程是分析具有相关响应的纵向数据的一种统计方法。该方法需要指定受试者结果变量重复测量的工作相关结构，如果正确指定了工作相关矩阵，则回归参数的GEE估计量将是最有效的。因此，需要在一组工作相关结构中选择最接近底层结构的工作相关矩阵。提出了准似然信息准则（quasulikelihood Information criteria， QIC）来选择GEE中工作相关结构和解释变量的最佳子集。然而，其选择真实相关结构的成功率已确定为29.4%左右。同样，过去的研究表明，它的偏差随着参数的增加而增加。考虑二元响应的纵向数据，通过数值模拟建立了QIC在选择真实工作相关结构时的一致性及其一致性条件。此外，我们提出了一种改进的QIC，对原始QIC中参数估计的数量进行惩罚，并通过数值验证了惩罚增强了QIC在选择真实工作相关结构时的一致性。结果表明，如果只考虑简约结构，QIC选择真实相关结构的概率接近1，否则无论样本量、被试人均测量量和相关水平的增加，选择率都小于50%。进一步，我们确定了当我们对估计的相关参数的数量进行惩罚时，选择真实相关结构r0的概率几乎肯定收敛于1。
The generalized estimating equations (GEE) is one of the statistical approaches for the analysis of longitudinal data with correlated response. A working correlation structure for the repeated measures of the outcome variable of a subject needs to be specified by this method and the GEE estimator for the regression parameter will be the most efficient if the working correlation matrix is correctly specified. Hence it is desirable to choose a working correlation matrix that is the closest to the underlying structure among a set of working correlation structures. The quasi-likelihood Information criteria (QIC) was proposed for the selection of the working correlation structure and the best subset of explanatory variables in GEE. However, its success rate in selecting the true correlation structure has been established to be about 29.4%. Likewise, past studies have shown that its bias increases with the number of parameters. By considering longitudinal data with binary response, we establish numerically through simulations the consistency property of QIC in selecting the true working correlation structure and the conditions for its consistency. Further, we propose a modified QIC that penalizes for the number of parameter estimates in the original QIC and numerically establish that the penalization enhances the consistency of QIC in selecting the true working correlation structure. The results indicate that QIC selects the true correlation structure with probability approaching one if only parsimonious structures are considered otherwise the selection rates are less than 50% regardless of the increase in the sample size, measurements per subject and level of correlation. Further, we established that the probability of selecting the true correlation structure R 0 almost surely converges to one when we penalize for the number of correlation parameters estimated.