Collaborative Research: Estimation and Testing for Associations with Multiple-Response Categorical Variables from Complex Surveys

当测量两个或多个分类变量时，自然会产生关于它们之间关联的问题。成熟的方法，如独立性的皮尔逊卡方检验和对数线性模型，已经发展到评估“单一反应”分类变量之间的关联结构。当这些分类变量中的一个来自于一个要求受访者“选择所有适用的”的调查问题时，分析就不那么直截了当了，因为调查受访者可能会对列表中的多个项目做出积极的回应，而这些回应很可能是相关的，从而产生了一个“多回应”分类变量。此外，当调查数据来自复杂的调查设计时，目前还没有统计分析方法可用于分析涉及多响应分类变量的关联结构。该研究项目将开发一套新的统计分析程序，用于测试和估计关联，并对复杂调查抽样产生的多反应分类变量进行建模。该研究将建立在最近开发的方法多响应分类变量在简单随机样本情况下。在分析复杂调查抽样中普通单反应分类变量之间的关联时常见的Rao-Scott调整将得到扩展，以发展涉及多反应分类变量的关联的pearson型检验。基于比值比的关联度量和相应的基于线性化的标准误差将被导出来度量关联水平。将开发边际广义对数线性模型，允许根据多响应分类变量所代表的因素的主要影响和相互作用来描述关联结构。基于模型的拟合优度检验和优势比估计将使用渐近技术进行开发。将通过模拟手段审查所制定的所有方法的适当性。社会上充斥着各种各样的调查，其中许多问题都是邀请受访者从一系列项目中“选择所有适用的”。这项研究将为调查分析人员提供一套基本的统计分析工具，用于分析这类问题的数据，目前还没有好的替代方法。它还将为未来的研究奠定基础，包括扩展到更多不同的数据结构和处理丢失的数据。由于调查是我们社会信息收集和交流系统中不可或缺的一部分，因此可以预期其影响将是深远的，影响到公共卫生、政治学、犯罪学、社会学、人口统计学、商业和技术等领域。任何使用统计设计的调查并包括“选择所有适用的”问题的机构都将从本研究提供的工具中受益。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。

When two or more categorical variables are measured, questions naturally arise regarding the associations among them. Well-established methods, such as Pearson chi-square tests for independence and loglinear models, have been developed to assess the association structure between "single-response" categorical variables. When one of these categorical variables arises from a survey question which asks respondents to "choose all that apply," the analysis is not as straightforward because survey respondents may respond positively to more than one item from the list and the responses are likely to be correlated, creating a "multiple-response" categorical variable. Furthermore, when the survey data arises from a complex survey design, there currently are no statistical analysis methods available to analyze association structures involving multiple-response categorical variables. This research project will develop a new set of statistical analysis procedures for testing and estimating associations and modeling multiple-response categorical variables arising through complex survey sampling. The research will build upon recently developed methods for multiple-response categorical variables in the simple random sample case. Rao-Scott adjustments, common in the analysis of associations among ordinary single-response categorical variables from complex survey sampling, will be extended to develop Pearson-type tests of associations involving multiple-response categorical variables. Odds-ratio-based measures of association and corresponding linearization-based standard errors will be derived to measure level of association. Marginal generalized loglinear models will be developed that allow the association structure to be described in terms of main effects and interactions due to the factors represented by the multiple-response categorical variables. Model-based tests for goodness-of-fit and estimates of odds ratios will be developed using asymptotic techniques. Adequacy of all methods developed will be examined by means of simulation.Society is inundated with surveys, many of which include questions that invite respondents to "choose all that apply" from a series of items. This research will provide survey analysts with an essential set of statistical analysis tools for analyzing data from questions of this type, for which there currently is no good alternative. It also will lay the groundwork for future research including extensions to more varied data structures and the handling of missing data. Because surveys are such an integral part of our society's information-gathering and exchange system, the impact can be expected to be far-reaching, affecting areas such as public health, political science, criminology, sociology, demography, business, and technology. Any institution that uses statistically-designed surveys and includes "choose all that apply" questions stands to benefit from the tools provided by this research. 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.