This paper proposes a multivariate ordered response system framework to model the interactions in non-work activity episode decisions across household and non-household members at the level of activity generation. Such interactions in activity decisions across household and nonhousehold members are important to consider for accurate activity-travel pattern modeling and policy evaluation. The econometric challenge in estimating a multivariate ordered-response system with a large number of categories is that traditional classical and Bayesian simulation techniques become saddled with convergence problems and imprecision in estimates, and they are also extremely cumbersome if not impractical to implement. We address this estimation problem by resorting to the technique of composite marginal likelihood (CML), an emerging inference approach in the statistics field that is based on the classical frequentist approach, is very simple to estimate, is easy to implement regardless of the number of count outcomes to be modeled jointly, and requires no simulation machinery whatsoever.