## Statistical Methods for Modeling Land

From a human economic perspective, one of the most pertinent factors in land-use decisions is land value. Determinants of land markets have been extensively studied to quantify individual preferences for property attributes. One commonly employed method, hedonic analysis, uses the sale price of a parcel as a proxy for measuring individual willingness to pay for structural and locational property variations. A multiple regression approach is used to estimate the property price based on a suite of attributes. Table 1 provides a list of common covariates grouped into three categories: structural, neighborhood, and environmental. Equation [1] illustrates a general specification of a hedonic model structure:

 Ecological/ Structural Neighborhood environmental attributes attributes attributes Square footage Distance to Proximity to open No. of bedrooms downtown, space No. of bathrooms airport, etc. Air quality School district Water quality Age of house Crime Landscape metrics Type of garage Demographic profile

where Pi — price, h — an intercept variable, — vectors of coefficients for the model variables, and e, — standard regression error term.

A multiple regression approach has also been used to estimate the demand for quantities ofparticular land-use types. The area ofinterest is divided into a set ofdiscrete zones (e.g., block group, traffic analysis zone), and an array of predictor variables is used to estimate the area of land use by type. The dependent variable in this case, the area of each type of land use, is estimated with some combination of social, economic, and environmental variables specified in much the same way as the hedonic price model discussed above. While these approaches may be useful for explaining consumer preferences and historical land-use patterns, they have limited predictive ability to capture the nonlinear and emergent behavioral patterns that characterize urban transformation (e.g., edge cities).

Discrete choice analysis models the probability of a specific outcome from the set of alternatives that constrain a decision-making process. This technique commonly employs a binomial or multinomial statistical model, such as logit (see eqn [2]) or probit, where decisions are represented by a maximum likelihood or random utility function that is defined by independent variables whose values are estimated based on the actual decisions ofindividuals when faced with similar choices. Choice sets can be continuous or discrete and can occur as a single decision or within a nested structure. An example ofthe former would be representing a development event binomially, while the latter would be a choice between development and no development, followed by a nested choice within the development branch between commercial or residential.

The logistic regression or logit function is given by

where E(Y) — the expected response value, ho — an intercept variable, and — coefficient representing estimated odds ratios for variable Xn holding all else constant.

While these statistical approaches could serve as stand-alone models of land-use change, they are more commonly employed as components of more complex models. For example, the California Urban Futures (CUF) model uses a regression approach to calibrate the land-use change submodel against historical land-use changes using population and employment growth, proximity to employment, commercial and industrial land uses, and spatial and topographic factors as independent variables. Another example is UrbanSim, where hedonic analysis is used to estimate the land price model and a multinomial logit model is used to estimate probabilities that households and firms will occupy a particular parcel. Finally, discrete choice models are commonly employed in travel demand, cellular automata (CAs), and agent-based models, which are discussed below, and are particularly used to calibrate parameters from empirical data.

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