Questions that ask respondents to "choose all that apply" from a set of items occur frequently in surveys. Categorical variables that summarize this type of survey data are called multiple response (or pick any/c) categorical variables. It is often of interest to test for independence between two categorical variables. When categorical variables can have multiple responses, traditional Pearson chi-square tests for independence should not be used because of the within-subject dependence among responses. This research will provide methods to test for independence between two or more multiple-response categorical variables. A modified version of the Pearson statistic will perform the test, and bootstrap procedures will provide approximate sampling distributions. First and second-order corrections will allow for chi-square distribution approximations to the sampling distribution. Generalized log linear models and multivariate binomial logit-normal models will provide a model-based approach for the test of independence.
Many survey questions are asked in a multiple-response manner. Examples include: "What types of cars do you own?" and "For what criminal offenses have you been arrested?" Other questions naturally fall into a multiple-response format, but some researchers avoid asking them in this format due to statistical analysis problems. For example, most survey questions dealing with ethnicity allow respondents to make only one choice, which is entirely inappropriate in today's highly multicultural population. Other researchers may analyze multiple-response questions as if they came from single-response categorical variables, which can lead to very conservative tests of independence. This research will allow researchers to incorporate these types of questions into surveys and use statistically correct methods of analysis. The research is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies under the Research on Survey and Statistical Methodology Funding Opportunity.
