Generalized Linear Models

本建议侧重于在抽样调查、交通研究、生态调查和临床试验中选择实验或观察单位的数学模型。PI研究了单位自动生成的概念，即事件发生的标记点过程，被解释为观测单位，标记包含所有相关的定量信息。这是用于市场研究和动物行为调查等情况的概率模型，其中每个抽样单位是具有随机类型或标记的事件，包括协变量和响应。由于单元数和协变量配置都是随机的，因此在计算响应分布时必须小心，因为对点过程进行采样的不同方案会产生不同的采样分布。抽样方案可能有偏差，因为它倾向于较大的响应值。从二元随机效应模型中抽取的样本可能会出现不太明显的偏差。例如，其他事件的协变量值可能会产生干扰。此外，从固定协变量地层中取配额样本的单元的响应分布不必与具有相同协变量值的自动生成单元的条件分布相同。在传统的田间试验统计公式中，将单元集视为事先固定的，对固定的单元随机分配处理。在调查工作中，样本单位是通过客观的随机化机制从总体中选择的，与应答无关。相比之下，在动物行为研究中，每个行为事件都是一个单位，单位的数量和配置都没有预先规定。在临床试验中，患者不是预先固定的，也不是随机抽样选择的。相反，他们是志愿者，在某种程度上是自我选择的，并且经常接受预先筛选以提高依从率。这项工作的目的是开发适合这类偏抽样方案的概率方案，其中抽样单位之间的响应分布可能不同于更广泛人群中的响应分布。

This proposal focuses on mathematical models for the selection of experimental or observational units in sample surveys, traffic studies, ecological surveys and clinical trials. The PI studies the concept of auto-generation of units, a marked point process for the occurrence of events, interpreted as observational units, the mark incorporating all relevant quantitative information. This is intended as a probabilistic model for situations such as marketing studies and animal behaviour surveys, where each sampling unit is a event having a random type or mark, including both covariate and response. Since the number of units and the covariate configuration are both random, care must be taken in calculating the response distribution because different schemes for sampling the point process yield different sampling distributions. The sampling scheme may be biased in the sense that it favours larger values of the response. Less obvious biases may occur in samples drawn from binary random-effects models. For example, there may be interference from the covariate value for other events. Moreover, the response distribution for a unit taken by quota sample from a fixed covariate stratum need not be the same as the conditional distribution for an autogenerated unit having the same covariate value.In the traditional statistical formulation taken from field trials, the set of units is regarded as fixed in advance, and treatment is assigned at random to those fixed units. In survey work, the sample units are selected from the population by an objective randomization mechanism independent of the response.By contrast, in animal behaviour studies, each behaviour event is a unit, and neither the number nor the configuration of units is pre-specified. In clinical trials, the patients are not fixed in advance, nor are they selected by random sampling. Instead, they are volunteers, to some extent self-selected, and frequently subject to pre-screening to improve compliance rates. The aim of this work is to develop probabilistic schemes tailored to biased-sampling schemes of this sort, where the response distribution among sampled units may be different from the response distribution in the broader population.