This paper examines the endogenous relationship between residential level of accessibility and household trip frequencies to tease out the direct and indirect effects of observed behavioural differences. We estimate a multivariate ordered probit model system, which allows dependence in both observed and unobserved factors, using data from the 2016 Transportation Tomorrow Survey (TTS), a household travel survey in the Greater Golden Horseshoe Area (GGH) in Toronto. The modelling framework is used to analyse the influence of exogenous variables on eight outcome variables of accessibility levels and trip frequencies by four modes (auto, transit, bicycle and walk), and to explore the nature of the relationships between them. The results confirm our hypothesis that not only does a strong correlation exist between the residential level of accessibility and household trip frequency, but there are also direct effects to be observed. The complementarity effect between auto accessibility and transit trips, and the substitution effect observed between transit accessibility and auto trips highlight the residential neighbourhood dissonance of transit riders. It shows that locations with better transit service are not necessarily locations where people who make more transit trips reside. Essentially, both jointness (due to error correlations) as well as directional effects observed between accessibility and trip frequencies of multiple modes offer strong support for the notion that accessibility and trip frequency by mode constitute a bundled choice and need to be considered as such.