标题： 具有正态分布和共轭随机效应的广义线性模型族用于重复测量 显示英文标题

标题： A Family of Generalized Linear Models for Repeated Measures with Normal and Conjugate Random Effects

摘要： 非高斯结果通常使用所谓的指数族的成员来建模。著名的成员包括用于二元数据的伯努利模型（导致逻辑回归）和用于计数数据的泊松模型（导致泊松回归）。扩展这一族的主要原因有两个：（1）过离散现象的发生，这意味着数据中的变异性无法被模型充分描述，而这些模型通常表现出规定的均值-方差关系；（2）适应数据中的分层结构，这种结构来源于数据中的聚类，而这又可能源于多次测量结果，例如同一家庭的不同成员等。第一个问题通过各种过离散模型来处理，例如用于分组二元数据的 beta-二项式模型和用于计数数据的负二项式模型。聚类通常通过引入随机的个体特定效应来解决。虽然并非总是如此，但人们通常假设这些随机效应服从正态分布。尽管这两种现象可能同时发生，但结合它们的模型并不常见。本文提出了一类广义线性模型，通过两组独立的随机效应来处理过离散和聚类问题。我们特别强调了第一方面（均值层面的共轭随机效应）和第二方面（嵌入线性预测器中的正态随机效应），尽管我们的模型族更为通用。我们特别关注二元、计数和事件时间案例。除了模型构建外，我们还概述了估计方法，并最终选择了具有解析-数值积分的最大似然估计法。讨论了边际相关函数推导的影响。该方法应用于癫痫发作研究的数据、一项名为甲真菌病的趾甲感染临床试验数据以及患有哮喘儿童的生存数据。 显示英文摘要

摘要： Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean--variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper proposes a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary, count and time-to-event cases are given particular emphasis. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic--numerical integration. Implications for the derivation of marginal correlations functions are discussed. The methodology is applied to data from a study in epileptic seizures, a clinical trial in toenail infection named onychomycosis and survival data in children with asthma.