Bayesian analysis of a two-way categorical table incorporating intraclass correlation
Bayesian analysis of a two-way categorical table incorporating intraclass correlation
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包含类内相关性的双向分类表的贝叶斯分析
DOI：
10.1080/10629360500108962
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发表时间：
2006
影响因子：
1.2
通讯作者：
J. Choi
中科院分区：
文献类型：
--
作者：
B. Nandram;J. Choi
分析单个多项式表中的数据非常简单。具体地说，对于双向分类表的分析，两个变量之间的常见卡方独立性检验和单元概率的最大似然估计是现成的。当双向分类表中的计数是由家族数据(相关数据的集群)形成时，常见的卡方检验不再适用。我们注意到，对常见的卡方检验有几次近似调整。例如，Choi和McHugh(Choi，J.W.和McHugh，R.B.，1989)在聚类和加权观测的拟合优度和独立性检验中的折减因子。生物识别，45,979-996。)演示了如何调整聚集数据和加权数据的卡方统计。然而，我们的主要贡献是构建和分析贝叶斯模型，该模型去掉了所有的解析近似。这是标准多项Dirichlet模型的扩展，以包括与集群中的个体相关联的组内相关性。我们使用了Altham(Altham，P.M.，1976)所描述的关键公式，离散变量分析对分组为家庭的个体进行了分析。比普里斯卡，63,263-269。)以纳入组内相关性。这种类内相关性随集群的大小而变化，但我们假设对于相同变量的相同大小的所有集群，这种相关性是相同的。我们使用马尔可夫链蒙特卡罗方法来拟合我们的模型，并对类内相关性和细胞概率进行后验推断。利用蒙特卡罗积分和二项式重要性函数，我们得到了无相关性检验的贝叶斯因子。为了证明替代测试和评估程序的性能，我们使用了来自国家健康访谈调查和模拟研究的关于活动限制状态和年龄的数据。
It is straightforward to analyze data from a single multinomial table. Specifically, for the analysis of a two-way categorical table, the common chi-squared test of independence between the two variables and maximum likelihood estimators of the cell probabilities are readily available. When the counts in the two-way categorical table are formed from familial data (clusters of correlated data), the common chi-squared test no longer applies. We note that there are several approximate adjustments to the common chi-squared test. For example, Choi and McHugh (Choi, J.W. and McHugh, R.B., 1989, A reduction factor in goodness-of-fit and independence tests for clustered and weighted observations. Biometrics, 45, 979–996.) showed how to adjust the chi-squared statistic for clustered and weighted data. However, our main contribution is the construction and analysis of a Bayesian model which removes all analytical approximations. This is an extension of a standard multinomial-Dirichlet model to include the intraclass correlation associated with the individuals within a cluster. We have used a key formula described by Altham (Altham, P.M., 1976, Discrete variable analysis for individuals grouped into families. Biometrika, 63, 263–269.) to incorporate the intraclass correlation. This intraclass correlation varies with the size of the cluster, but we assume that it is the same for all clusters of the same size for the same variable. We use Markov chain Monte Carlo methods to fit our model, and to make posterior inference about the intraclass correlations and the cell probabilities. Also, using Monte Carlo integration with a binomial importance function, we obtain the Bayes factor for a test of no association. To demonstrate the performance of the alternative test and estimation procedure, we have used data on activity limitation status and age from the National Health Interview Survey and a simulation study.