Surveys often contain qualitative variables for which respondents may select any number of the outcome categories. This type of response is called multiple responses. Each outcome category refers to an item, where the items are dependent. Agresti and Liu (2001) introduced marginal models based on the marginal counts of each item. The models describe the association between items and some explanatory variables taking the dependence into account. The model fitting has at least two approaches. One is called the generalized estimation equations (GEE) method and the other is called the maximum likelihood (ML) estimation for homogeneous linear predictor (HLP) models (Lang, 2005).
We will discuss MMI hypothesis testing, dually consistent odds ratio estimators, more efficient use of correlation estimation for GEE and deletion diagnostics for ML and GEE estimation. Estimation of the odds ratio for stratified multiple responses for sparse data having dependent or independent strata will also be discussed. An extension of multiple responses are repeated multiple responses. Model approaches will be outlined as well as future work.