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Center for Nonlinear Studies |
Multiple-response categorical variables (MRCVs) are common in surveys where respondents are instructed to ”mark all that apply” from a list of items. As is common with categorical variables, questions may be asked regarding the association between a MRCV and other variables. Standard statistical analyses based on contingency tables cannot be used with MRCVs, however, because of the lack of independence among the multiple responses from one unit. Because responses to a MRCV form a binary vector whose length is the number of items is the list, methods for correlated binary data can be applied. When the total number of items in one analysis becomes large, however, the data become sparsely distributed in a high-dimensional space. Marginal generalized loglinear models are proposed that allow the associations between items of different MRCVs to vary across levels of the MRCVs in structured ways, while reducing the number of parameters to be estimated relative to a full loglinear model. Associations can be modeled to depend on the levels of the different MRCVs in a classical factorial structure or in other specified ways. An example from a survey of Kansas farmers demonstrates how the models can be used. Extensions to data from complex survey samples are discussed. This research was partially supported by SES-0233321 and SES-0418688 from NSF.