The growing availability of geotagged big data has stimulated substantial discussion regarding their usability in detailed travel behaviour analysis. Whilst providing a large amount of spatio-temporal information about travel behaviour, these data typically lack semantic content characterising travellers and choice alternatives. The inverse discrete choice modelling (IDCM) approach presented in this paper proposes that discrete choice models (DCMs) can be statistically inverted and used to attach additional variables from observations of travel choices. Suitability of the approach for inferring socioeconomic attributes of travellers is explored using mode choice decisions observed in London Travel Demand Survey. Performance of the IDCM is investigated with respect to the type of variable, the explanatory power of the imputed variable, and the type of estimator used. This method is a significant contribution towards establishing the extent to which DCMs can be credibly applied for semantic enrichment of passively collected big data sets while preserving privacy.