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Spatial Models in Marketing

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

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Spatial Models in Marketing

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

  2. 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

  3. 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

  4. 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?

  5. Modeling spatial effects • General specification • 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 Spatial drift Spatial lags Spatially correlated errors

  6. 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

  7. 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

  8. 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

  9. 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)

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