Application of eigenvector-based spatial filtering approach to a multinomial logit model for land use data

The present study builds a spatial statistical model for estimating land use maps. Many approaches for modeling land use maps exist in the literatures. A representative method includes a multinomial logit model (Miller and Plantinga, 1999), in which the likelihood of placing each land use category, such as land for building and forest, into each zone is explained by selected attributes such as population and elevation. Because neighboring zones tend to be categorized into the same land use class, considering spatial dependence among zones is important when applying a multinomial logit model for modeling land use maps. Although previous studies involving spatial econometric techniques attempted to consider spatial dependence by using a spatial weight matrix, such methods require a computationally burdensome iterative calculation for parameter estimation (e.g., the expectation-maximization algorithm or the Markov chain Monte Carlo method). On the contrary, the present study employs eigenvector-based spatial filtering based on a spatial statistical approach, in which parameters are estimated using the standard maximum likelihood method for modeling spatial dependence. This is easy to implement using standard statistical software packages. Moreover, while analyzing land use, it is essential that the filtering method enable visualization of secular changes in spatial patterns influencing the choice of each land use category at each instance. The results suggest that compared to conventional nonspatial multinomial logit models, the predictive power in terms of the Akaike information criterion (AIC) is substantially improved with spatial filtering.