Long-distance travel demand models have traditionally been estimated based only on national travel surveys (NTS). However, low response rate is an increasing issue in NTS data, calling into question the representativeness of the survey sample. In this paper we investigate which machine learning method (if any) is a suitable approach to model transportation mode choice for long-distance travel based on NTS data complemented by mobile phone network data. We find artificial neural network (ANN) to be the best candidate, and that for an ANN to be feasible as a mode choice model intended for policy development, the network architecture should fulfill a set of requirements: a utility function inspired network architecture, correct handling of non-available alternatives, and constraining the weights connected to the travel cost inputs to be the same for all modes. Furthermore, complementing NTS data with mobile phone network data provides more stable and feasible valuations of travel time compared to using NTS data only.