Regression Diagnostics in Survey Data

线性回归模型的诊断作为选项包含在许多统计软件包中，现在可供分析人员随时使用。然而，这些工具通常针对普通或加权最小二乘回归，而不考虑分层、聚类和调查权重，这些是复杂样本调查中收集的数据集的特征。普通的最小二乘诊断会误导用户，因为模型参数估计的方差通常会被标准程序错误地估计。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应调查数据，并在必要时开发新的诊断方法。该项目还将研究现有线性回归诊断在应用于复杂调查数据时的特性。需要扩展来覆盖聚集和非聚集数据。要研究的具体技术是：线性回归的杠杆及其影响的启发式截止点；杠杆分布，包括直方图和分位数；修改对模型参数估计和预测值影响的单位删除措施，以及用于确定有影响的观测值的经验法则；由于删除一个或一组观测值而引起的标准误差估计的变化；并扩展了共线性诊断，包括方差膨胀因子和参数估计的方差分解。由美国政府机构和其他国内和国际组织赞助的许多调查收集的数据用于拟合统计模型。这些模型用于了解疾病、失业、教育成就水平和其他主题之间的相关性。这些调查通常是分层的、单阶段或多阶段的调查，其中各单位的调查权重可能有很大的不同。实质性领域的一些例子是医疗条件、医疗保健支出、家庭和儿童的社会福利以及教育进展状况。评估和改进现有的模型拟合和诊断方法是重要的，以便充分利用这些调查中收集的数据，并避免可能产生误导或错误的结论。作为支持调查和统计方法研究的联合活动的一部分，该研究得到了方法、测量和统计计划和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.