基于有序分类响应变量的多重比较过程和样本量确定问题的研究

Multiple comparison procedures, which are used to compare diffence of different groups, have long been important techniques in the research of many disciplines including medical science, psychology and social sciences. However there is shortage of rigorous statistical theory and method for multiple comparisons with ordered categorical responses. The method of latent variable model that conceptualizes the ordinal responses as manifestations of some underlying continuous variable is used to conduct multiple comparisons of several treatments with a control with ordered categorical responses, but most of the latent models are assumed to be normal distribution or logistic distribution. In this project, we will discuss multiple comparison procedures for a unified latent variable model such as location-scale distribution with ordered categorical data, and the relationship between the latent unified model and the existing methods will be explored. Also, sample size determination for the multiple comparison procedures will also be discussed.

多重比较被用来检验多组独立样本的差异性，在医学、心理学、社会学等各个学科中均有广泛的应用，然而对具有有序分类响应变量的多重比较问题的研究还缺乏严谨的统计理论和方法。潜变量模型方法把有序分类响应变量看作是某个连续随机变量的一个实现,它已经被应用于构造具有有序分类响应变量的含有控制组的多重比较过程中，而在已有的研究中潜变量模型一般被假定为服从正态分布或是logistic分布。本项目将会用统一的潜变量模型如位置尺度参数模型来模拟有序分类数据从而实现多组独立样本的多重比较过程，并探索已有的多重比较过程与统一的潜变量模型方法之间的关系，以及对满足一定功效的多重比较过程的最优样本量问题进行讨论。

本项目遵照计划书来执行，基本完成了预期目标。研究成果如下：首先，基于潜变量模型探讨具有有序分类响应变量的多重比较问题，把向上逐步检验法应用到多个实验组与一个控制组的多重比较问题中，提高了检验过程的功效。其次，基于所介绍的向上逐步检验过程，我们对满足一定功效性的多重比较过程的最优样本量问题进行了探讨，从而方便了研究员在实验设计过程中对样本量的选择，达到精简人力、物力、财力投入的目的，具有很强的实用价值。