The Huff model (Huff 1962, 1963, 1964) is the most popular spatial interaction model for retailing and services and belongs to the family of probabilistic market area models. The basic idea of the model, derived from the Luce choice axiom, is that consumer decisions are not deterministic but probabilistic. Thus, the decision of customers for a shopping location in a competitive environment cannot be predicted exactly. The results of the model are probabilities for these decisions (interaction probabilities), which can be interpreted as market shares of the regarded locations (\(j\)) in the customer origins (\(i\)), \(p_{ij}\) (local market shares). The model results can be regarded as an equilibrium solution (consumer equilibrium) with logically consistent market shares (0 < \(p_{ij}\) < 1, \(\sum_{j=1}^n{p_{ij} = 1}\)). From a theoretical perspective, the model is based on an utility function with two explanatory variables ("attraction" of the locations, transport costs between origins and locations), which are weighted by an exponent: \(U_{ij}=A_{j}^\gamma d_{ij}^{-\lambda}\). The probability is calculated as the utility quotient: \(p_{ij}=U_{ij}/\sum_{j=1}^n{U_{ij}}\). The distance decay function reflecting the disutility of transport costs can also be exponential or logistic. The model can also be used for the estimation of market areas based on location sales or total patronage using nonlinear optimization algorithms. When the "real" local market shares were observed, the model can be parametrized by using the Multiplicative Competitive Interaction (MCI) Model.
The Multiplicative Competitive Interaction (MCI) Model (Nakanishi/Cooper 1974, 1982) is an econometric model for analyzing market shares and/or market areas in a competitive environment where the market is divided in \(i\) submarkets (e.g. groups of customers, time periods or geographical regions) and served by \(j\) suppliers (e.g. firms, brands or locations). The dependent variable of the model is \(p_{ij}\), the market shares of \(j\) in \(i\), which are logically consistent (0 < \(p_{ij}\) < 1, \(\sum_{j=1}^n{p_{ij} = 1}\)). The market shares depend on the attraction/utility of the alternative \(j\) in the choice situation/submarket \(i\), \(A_{ij}\) or \(U_{ij}\). The model is nonlinear (multiplicative attractivity/utility function with exponential weighting) but can be transformed to be estimated by OLS (ordinary least squares) regression using the multi-step log-centering transformation. Before the log-centering transformation can be applied, which is required for fitting the model, also a re-arrangement of the raw data (e.g. household surveys) in an interaction matrix is necessary. An interaction matrix is a special case of table where every row is an \(i\) x \(j\) combination and the market shares of \(j\) in \(i\) (\(p_{ij}\)) are saved in a new column (Linear table, the opposite of crosstable). The MCI model is a special case of market share model (which fulfills the requirement of logical consistency in the output), but can especially be used as a market area model (or spatial MCI model) in retail location analysis since it is an econometric approach to estimate the parameters of the Huff model mentioned above.
The functions in this package include fitting the MCI model, MCI shares simulations, the log-centering transformation of MCI datasets, creation of interaction matrices from empirical raw data and several tools for data preparation. Additionally, the package provides applications for the Huff model, including a nonlinear optimization algorithm to estimate market areas on condition that total market areas (customers, sales) of the stores/locations are known.
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