Download - 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– 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?
,Z,X|yf
)),(,0(~ , ZNeeXy
,,X| yZf
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
)),(,0(~ ,][ ZNeeZXWyy
Spatial lags
Spatial drift
Spatially correlated errors
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
)),(,0(~ ,][ ZNeeZXWuu
)),(,0(~)( ),(],[)()( ZNtetetZXtWyty
))')(,()(,0(~ ,])[( 111 WIZWINvvXWIy
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
• 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
I),0(~ ,)( 2222 NeeX
Research opportunities
I)N(0, ~ ,)( 2111 eeXy
Error component that follows a spatial lag pattern
Marketing mix variables are a function of the error term
Marketing mix variables
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)