Regression Diagnostics in Survey Data

线性回归模型的诊断包括在许多统计程序包中，现在分析师可以很容易地获得。然而，这些工具一般针对普通或加权最小二乘回归，没有考虑作为复杂抽样调查中收集的数据集的特征的分层、聚类和调查权重。普通的最小二乘诊断法可能会误导用户，因为标准程序通常会错误地估计模型参数估计的方差。方差或标准误差估计是许多诊断的重要组成部分。这项研究将使现有的诊断方法适用于调查数据，并在必要时开发新的诊断方法。本项目还将研究现有的线性回归诊断方法在应用于复杂调查数据时的特性。需要扩展才能同时涵盖集群数据和非集群数据。要研究的具体技术包括：利用线性回归及其启发式截止值进行影响；杠杆的分布，包括直方图和分位数；修改单位删除测量对模型参数估计和预测值的影响，以及用于识别有影响的观察的经验法则；因删除一个或多组观察而改变标准误差估计；以及扩展共线性诊断，包括用于参数估计的方差膨胀因子和方差分解。在美国政府机构和其他国内和国际组织赞助的许多调查中收集的数据用于拟合统计模型。这些模型被用来理解疾病、失业、教育成就水平和其他主题的相关性。这些调查通常是分层的、单一的或多阶段的调查，其中单位的调查权重可以有很大的不同。一些实质性领域的例子包括医疗条件、医疗支出、家庭和儿童的社会福利以及教育进展情况。评估和改进现有的模型拟合和诊断方法很重要，以便最大限度地利用在这些调查中收集的数据，并避免可能具有误导性或错误的结论。作为支持调查和统计方法研究的联合活动的一部分，这项研究得到了方法学、测量和统计计划和一个联邦统计机构联盟的支持。

Diagnostics for linear regression models are included as options in many statistical packages and now are readily available to analysts. However, these tools are generally aimed at ordinary or weighted least squares regression and do not account for stratification, clustering, and survey weights that are features of data sets collected in complex sample surveys. The ordinary least squares diagnostics can mislead users because the variances of model parameter estimates will usually be estimated incorrectly by the standard procedures. The variance or standard error estimates are an intimate part of many diagnostics. This research will adapt existing diagnostics for use with survey data, and, where necessary, develop new ones. This project also will study the properties of existing linear regression diagnostics when they are applied to complex survey data. Extensions are needed to cover both clustered and unclustered data. The particular techniques to be studied are: leverages for linear regression and their heuristic cutoffs for influence; distributions of leverages, including histograms and quantiles; modification of unit-deletion measures of influence on model parameter estimates and predicted values and the rules-of-thumb used to identify influential observations; change in standard error estimates due to deletion of an observation or groups of observations; and extension of collinearity diagnostics, including variance inflation factors and variance decompositions for parameter estimates.The data collected in many surveys sponsored by U.S. government agencies and other domestic and international organizations are used to fit statistical models. These models are used to understand the correlates of disease, unemployment, education achievement levels, and other topics. The surveys are typically stratified, single or multistage surveys where units can have substantially different survey weights. Some examples of substantive areas are medical conditions, expenditures for medical care, the social welfare of families and children, and the status of progress in education. Evaluation and improvements to existing methods of model-fitting and diagnosis are important in order to make the most of the data that are collected in these surveys and to avoid conclusions that may be misleading or erroneous. The research is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.