This article discusses modelling strategies for repeated measurements of multiple response variables. Such data arise in the context of categorical variables where one can select more than one of the categories as the response. We consider each of the multiple responses as a binary outcome and use a marginal (or population-averaged) modelling approach to analyse its means. Generalized estimating equations are used to account for different correlation structures, both over time and between items. We also discuss an alternative approach using a generalized linear mixed model with conditional interpretations. We illustrate the methods using data from a panel study in Australia called the Household, Income, and Labour Dynamics Survey.