Spatial Models in Marketing Bradlow et al 2005

Spatial Models in Marketing Bradlow et al (2005) Marketing Letters

Introduction • Interdependent entities – Consumers’ satisfaction ratings (Mittal et al 2004) – Retailers’ promotional policies (Bronnenberg and Mahajan 2001) • Objectives of this review paper – – Define elements of a spatial model Introduce various types of spatial models Model spatial effects Suggest new research directions

Elements of a spatial model • A map describes the relationship among individuals – Geographic, demographic, or psychometric • Distance metrics determine the strength of a relationship – Discrete or continuous – Isotropic: relationship depends on the distance, not on the direction – Individuals of shorter distance have a stronger relationship • Spatial distance results in a spatial effect

Types of spatial models • Type I models: – Predict the choice outcome y, conditional on the X variables and the map locations Z – Simplest specification: • Kriging: Predict the outcome variable of one individual at a specified location by using the known responses and locations of all other individuals. • Type II models: – Predict the locations Z at which certain outcomes occurred – Not generally discussed * Opportunity for ABM?

Modeling spatial effects • General specification Spatial drift Spatial lags Spatially correlated errors – Spatial lags • Outcomes are spatially interdependent – Spatially correlated errors • Error terms are spatially interdependent – Spatial drift • Parameters are a function of an individual’s location on the map

Modeling spatial effects • Variations – Replace choice outcome y with continuous latent utility u: – Spatio-temporal models: incorporate cross-sectional time series data: • Statistical Issues – Outcome variables y are (1) spatially correlated and (2) spatially-lagged dependent

Research opportunities • Dimensionality – Sheer amount of information that must be stored • GIS software, Matlab spatial statistics toolbox, Markov random field – Estimation • Simplify computations and reduce memory usage of likelihood-based approaches

Research opportunities • Analysis of marketing policies – Endogeneity between marketing mix and response variables • Spatial distribution depends on order of entry into the region and regional levels of advertising expenditure (Bronnenberg et al 2005). – Correction Marketing mix variables Error component that follows a spatial lag pattern Marketing mix variables are a function of the error term

Research opportunities • Interpretation of spatial effects – Impact of social influence on choice behavior (Yang and Allenby 2003; Bell and Song 2004) – Spatial priors in a hierarchical Bayes analysis to understand geographic dispersion of preference segments (Ter Hofstede et al 2002; Ter Hofstede 2004) – Group decision making (Arora 2004)