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Understanding food purchasing behaviours is complex because people make both choices among goods and volumes of those goods that they choose. We use the novel Multiple Discrete-Continuous Extreme Value (MDCEV) model, capable of handling both aspects of behaviour, on real-world food shopping behaviour data from a clinical trial. We compared the impact of providing general dietary advice, general dietary advice plus personalised shopping advice, or taxation, and combinations thereof, on the amount of saturated fat in consumers’ shopping baskets, using simulation. We used supermarket loyalty card data from a randomized controlled trial of 111 adults with raised cholesterol in Oxfordshire (UK). A Danish fat tax simulation alone is less effective than the tax in combination with dietary and shopping advice. These data illustrate the potential of MDCEV models for these behaviours and, by extension, informing food policies.