Title: The flexible substitution logit
Description: Different instruments are relevant for different marketing objectives (category demand expansion or market share stealing). To help brand managers make informed marketing mix decisions, it is essential that marketing mix models appropriately measure the different effects of marketing instruments. Discrete choice models that have been applied to this problem might not be adequate because they possess the Invariant Proportion of Substitution (IPS) property, which imposes counter-intuitive restrictions on individual choice behavior. Indeed our empirical application to prescription writing choices of physicians in the hyperlipidemia category shows this to be the case. We find that three commonly used models that all suffer from the IPS restriction - the homogeneous logit model, the nested logit model, and the random coefficient logit model - lead to counter-intuitive estimates of the sources of demand gains due to increased marketing investments in Direct-to-Consumer Advertising (DTCA), detailing, and Meetings and Events (M&E). We then propose an alternative choice model specification that relaxes the IPS property - the so-called "flexible substitution" logit (FSL) model. The (random coefficient) FSL model predicts that sales gains from DTCA and M&E come primarily from the non-drug treatment (87.4% and 70.2% respectively), whereas gains from detailing come at the expense of competing drugs (84%). By contrast, the random coefficient logit model predicts that gains from DTCA, M&E and detailing all would come largely from competing drugs.