Structural Models of Complementary Choices

Extracting Complements and Substitutes from Sales Data: A Network Perspective

“…Note the P(•|•) in Equation ( 12) is an estimate of the probability in ( 8), and we can consider, for example, estimates (10) and (11). We also modify the normalisation method to propose a symmetric version -the substitutability measure, where sim s (j, i) = j ∈I (c) j ∩I (c) i P(a l j = 1|a l j = 1) P(a l i = 1|a l j = 1) ( p∈I (c) i P(a l i = 1|a l p = 1) 2 )( p∈I (c) j P(a l j = 1|a l p = 1) 2 ) .…”

On the motivations for the dual-use of electronic and traditional cigarettes

“…A typical undergraduate textbook would tend to focus on a simpler definition of a complement (substitute) as a negative (positive) cross-price elasticity of demand which tends to be associated with static single-agent problems and is also a less versatile definition as it requires data on prices: see Berry et al (2014) for more on the pros and cons of different definitions. It is worth noting here that there do exist demand analyses of electronic and traditional cigarettes.…”

“…To this end, we probe the nature of preferences by allowing smokers to self-categorize. Within the confines of this paper a complement (substitute) is defined as in Berry et al (2014): if A is a complement (substitute) for B then the value of product A increases (decreases) with the availability of product B. This definition is in turn based on Milgrom and Roberts (1990) who define complementarity as a positive crosspartial derivative of the utility function with respect to quantities and is also close to the definition in Brandenburger and Nalebuff (2011) who define complementarity as equivalent to super-additivity of the utility function.…”

Extracting complements and substitutes from sales data: a network perspective

“…Despite its practical importance, the algorithmic problem of identifying the relationship between products in retail is not well known. For a long time, researchers and practitioners have selected the set of possible complementary or substitute products by means of, for instance, field expertise and simple statistics, and the analysis has usually been restricted to a fairly small number of products [9,10]. Recent development and application of natural language processing and machine learning (ML) algorithms, especially those based on word embedding, bring in new visions and opportunities, which makes it possible to analyse thousands of products [11][12][13].…”