ABSTRACT Data with multivariate count responses frequently occur in modern applications. The commonly used multinomial-logit model is limiting due to its restrictive mean-variance structure. For instance, analyzing count data from the recent RNA-seq technology by the multinomial-logit model leads to serious errors in hypothesis testing. The ubiquity of overdispersion and complicated correlation structures among multivariate counts calls for more flexible regression models. In this article, we study some generalized linear models that incorporate various correlation structures among the counts. Current literature lacks a treatment of these models, partly because they do not belong to the natural exponential family. We study the estimation, testing, and variable selection for these models in a unifying framework. The regression models are compared on both synthetic and real RNA-seq data. Supplementary materials for this article are available online.

中文翻译：

---

多元计数数据的回归模型


摘要 现代应用中经常出现具有多变量计数响应的数据。常用的多项式 Logit 模型由于其限制性均值-方差结构而受到限制。例如，通过多项 Logit 模型分析最新 RNA-seq 技术的计数数据会导致假设检验出现严重错误。多元计数之间普遍存在的过度分散和复杂的相关结构需要更灵活的回归模型。在本文中，我们研究了一些广义线性模型，其中包含计数之间的各种相关结构。目前的文献缺乏对这些模型的处理，部分原因是它们不属于自然指数族。我们在统一的框架中研究这些模型的估计、测试和变量选择。在合成和真实 RNA-seq 数据上比较回归模型。本文的补充材料可在线获取。