Ekholm A, McDonald J W, Smith P W
Rolf Nevanlinna Institute, University of Helsinki, Finland.
Biometrics. 2000 Sep;56(3):712-8. doi: 10.1111/j.0006-341x.2000.00712.x.
Models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders. The w-order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterization supports likelihood-based inference for both regression parameters, relating marginal probabilities to explanatory variables, and association model parameters, relating dependence ratios to simple and meaningful mechanisms. Five types of association models are proposed, where responses are (1) independent given a necessary factor for the possibility of a success, (2) independent given a latent binary factor, (3) independent given a latent beta distributed variable, (4) follow a Markov chain, and (5) follow one of two first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, foremost a set of binary time series on auranofin therapy against arthritis. Likelihood-based approaches are contrasted with approaches based on generalized estimating equations. Association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.
多变量二元响应模型通过单变量边际概率和所有阶次的依赖比进行参数化。第w阶依赖比是w个二元响应的联合成功概率除以假设独立时的联合成功概率。这种参数化支持基于似然的推断，既可以用于回归参数（将边际概率与解释变量相关联），也可以用于关联模型参数（将依赖比与简单且有意义的机制相关联）。提出了五种类型的关联模型，其中响应情况如下：（1）在成功可能性的必要因素给定的情况下是独立的；（2）在潜在二元因素给定的情况下是独立的；（3）在潜在贝塔分布变量给定的情况下是独立的；（4）遵循马尔可夫链；（5）根据二元潜在因素的实现情况遵循两个一阶马尔可夫链之一。通过重新分析三个数据集来说明这些模型，其中最重要的是一组关于金诺芬治疗关节炎的二元时间序列数据集。基于似然的方法与基于广义估计方程的方法形成对比。由依赖比指定的关联模型与由优势比或相关系数指定的其他多变量二元响应模型形成对比。
