Generalized Linear Models

该提案侧重于在抽样调查、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研究单位自动生成的概念，事件发生的标记点过程，解释为观察单位，标记包含所有相关的定量信息。这是一种概率模型，适用于营销研究和动物行为调查等情况，其中每个抽样单位是一个具有随机类型或标记的事件，包括协变量和响应。由于单位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提取的样本可能会出现不太明显的偏差。例如，可能存在来自其他事件的协变量值的干扰。此外，从固定协变量分层中通过配额样本获取的单位的响应分布不需要与具有相同协变量值的自动生成的单位的条件分布相同。在来自田间试验的传统统计公式中，单位集合被视为预先固定的，并且治疗被随机分配给那些固定的单位。在调查工作中，样本单位是通过独立于反应的客观随机化机制从总体中选择的。相比之下，在动物行为研究中，每个行为事件都是一个单位，单位的数量和结构都没有预先规定。在临床试验中，患者并不是事先固定的，也不是随机抽取的。相反，他们是志愿者，在某种程度上是自我选择的，并经常接受预先筛选，以提高遵守率。这项工作的目的是开发概率方案量身定制的偏置抽样方案，这种抽样单位之间的响应分布可能是不同的响应分布在更广泛的人口。

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.