A novel theoretical framework for predicting the branching between roaming and bond fission channels in molecular dissociations is described and applied to the decomposition of acetaldehyde. This reduced dimensional trajectory (RDT) approach, which is motivated by the long-range nature of the roaming, bond fission, and abstraction dynamical bottlenecks, involves the propagation of rigid-body trajectories on an analytic potential energy surface. The analytic potential is obtained from fits to large-scale multireference ab initio electronic structure calculations. The final potential includes one-dimensional corrections from higher-level electronic structure calculations and for the effect of conserved mode variations along both the addition and abstraction paths. The corrections along the abstraction path play a significant role in the predicted branching. Master equation simulations are used to transform the microcanonical branching ratios obtained from the RDT simulations to the temperature- and pressure-dependent branching ratios observed in thermal decomposition experiments. For completeness, a transition-state theory treatment of the contributions of the tight transition states for the molecular channels is included in the theoretical analyses. The theoretically predicted branching between molecules and radicals in the thermal decomposition of acetaldehyde is in reasonable agreement with the corresponding shock tube measurement described in the companion paper. The prediction for the ratio of the tight to roaming contributions to the molecular channel also agrees well with results extracted from recent experimental and experimental/theoretical photodissociation studies.