MODELING MULTIVARIATE BINARY DATA WITH ALTERNATING LOGISTIC REGRESSIONS
MODELING MULTIVARIATE BINARY DATA WITH ALTERNATING LOGISTIC REGRESSIONS
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DOI：
10.2307/2337173
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发表时间：
1993-09-01
期刊：
影响因子：
2.7
通讯作者：
DIGGLE, P
中科院分区：
文献类型：
--
作者：
CAREY, V;ZEGER, SL;DIGGLE, P
多变量二进制数据的边际模型允许单独建模的解释变量的反应之间的关系;和对反应之间的关联。当前者是科学焦点时，一阶广义估计方程方法（Liang & Zeger，1986）易于实现，并给出回归系数的有效估计，尽管二元结果之间的关联估计可能效率低下。当关联模型是焦点时，使用二阶估计方程的响应和所有成对乘积的同时建模（普伦蒂斯，1988）也给出了关联参数的更有效估计。然而，随着集群规模变大，这个过程在计算上可能变得不可行。本文提出了一种替代方法，交替逻辑回归，同时回归的解释变量的反应，以及建模的两两之间的比值比的反应之间的关联。该算法在使用一阶广义估计方程估计回归系数的逻辑回归和使用适当偏移更新比值比参数的同一聚类中其他响应的每个响应的逻辑回归之间迭代。对于大小为n的聚类，交替逻辑回归涉及n（2）阶矩阵的评估和求逆，而不是二阶广义估计方程所需的n（4）阶矩阵。交替逻辑回归估计被证明是合理有效的相对于解决二阶方程在一些问题。新的方法说明了与癫痫发作患者的神经心理学测试的分析。
Marginal models for multivariate binary data permit separate modelling of the relationship of the response with explanatory variables; and the association between pairs of responses. When the former is the scientific focus, a first-order generalized estimating equation method (Liang & Zeger, 1986) is easy to implement and gives efficient estimates of regression coefficients, although estimates of the association among the binary outcomes can be inefficient. When the association model is a focus, simultaneous modelling of the responses and all pairwise products (Prentice, 1988) using second-order estimating equations gives more efficient estimates of association parameters as well. However, this procedure can become computationally infeasible as the cluster size gets large. This paper proposes an alternative approach, alternating logistic regressions, for simultaneously regressing the response on explanatory variables as well as modelling the association among responses in terms of pairwise odds ratios. This algorithm iterates between a logistic regression using first-order generalized estimating equations to estimate regression coefficients and a logistic regression of each response on others from the same cluster using an appropriate offset to update the odds ratio parameters. For clusters of size n, alternating logistic regression involves evaluation and inversion of matrices of order n(2) rather than n(4) as required for second-order generalized estimating equations. The alternating logistic regression estimates are shown to be reasonably efficient relative to solutions of second-order equations in a few problems. The new method is illustrated with an analysis of neuropsychological tests on patients with epileptic seizures.