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.
