Abstract. Urban expansion has been a hot topic not only in the management of sustainable development but also in the fields of remote sensing and GIS. Urban development is a complicated dynamic process involving in various actors with different patterns of behavior. Modeling an urban development pattern is the prerequisite to understand the process. This paper presents a preliminary spatial framework for such modeling and uses it for the analysis of a rapidly developing city. This framework starts with a multi-scale conceptual model, which aims to theoretically link planning hierarchy, multi-extent analysis and multi-resolution data. The multi-extent data analysis is the focus of this paper, which is divided into three scales: change probability (macro), change density (meso) and change intensity (micro). Multi-extent data analysis aims to seek distinguishing spatial determinants on three scales, which is able to bridge planning system and data scale. The data analysis is based on the integration of change patterns detection method and spatial logistic regression method. The former is utilized for univariate analysis and then hypothesis formation. The latter is employed for systematic modelling of multi-variables. The combination of both is proven to have strong capacity of interpretation. This framework is tested by a case study of Wuhan City, P.R.China. The multi-scale property discovered is helpful for understanding complicated process of urban development. [Key Words]: Spatial framework, scale, multi-extent, change pattern detection, logistic regression. 1.

An autologistic regression model consists of a linear regression of a response variable on explanatory variables and an auto-regression on responses at neighboring locations on a lattice.

We investigate the spread of Nectria canker of beech which is a fungal chronic disease caused by Nectria ditissima Tul. et C. Tul. Data are available from a beech provenance trial. A possible influential factor on the proportion of infected trees per plot is the wind dispersal zone (wdz), a categorical variable describing the distance and wind direction from diseased shelter wood, the source of infection. We investigate the e#ect of wdz and whether the disease incidence in the regeneration can be explained alone by the wdz using di#erent approaches accounting for spatial correlation in the data. One method uses generalised estimation equations (GEEs) where through specification of a general variance-covariance matrix allowing for non-independence, spatial correlation can be accounted for in the model. The second method uses generalised additive models (GAMs) and the spatial autocorrelation is dealt with by modelling it as a spatial trend. The third method uses generalised linear mixed models (GLMM) with a random e#ect accounting for spatial correlation and heterogeneity. We show that in the beech data some spatial correlation is present, which is over and above that accounted for by the wdz's. Hence methods not accounting for this correlation are inappropriate. The GLMM is the most appropriate model because it manages to model the biological process best: It explains the variation in disease incidence by the wdz and by secondary infection. Hence it yields the most precise estimates.

Prior work has shown the strong presence of regional and spatial context in linkages between regime characteristics and involvement in civil and international conflict, but no adequate statistical model has explicitly captured these forces. Models that adequately reflect the interdependence of actors and actions in world politics are faced with difficult problems of estimation since the classical likelihood becomes intractable in the presence of the dependencies among observations. Most current solutions to this problem are based on approaches that were developed decades ago during a period of expensive computing. However, these approaches are no longer neither necessary nor appropriate. Using data from 1988, we use an autologistic formulation, estimated by Monte Carlo Markov Chain approximation, to extend our work exploring the link between authority structures and peace, one of the most salient present research topics in international relations. Our estimated model allows us to predict about half of the violent domestic and international conflicts that emerged in the subsequent decade.

An autologistic regression model consists of a logistic regression of a response variable on explanatory variables and an auto-regression on responses at neighboring locations on a lattice. It is a Markov random field with pairwise spatial dependence and is a popular tool for modeling spatial binary responses. In this article, we add a temporal component to the autologistic regression model for spatialtemporal binary data. The spatial-temporal autologistic regression model captures the relationship between a binary response and potential explanatory variables, while adjusting for both spatial dependence and temporal dependence simultaneously by a space-time Markov random field. We estimate the model parameters by maximum pseudo-likelihood and obtain optimal prediction of future responses on the lattice by a Gibbs sampler. For illustration, the method is applied to study the outbreaks of southern pine beetle in North Carolina. We also discuss the generality of our approach for modeling other types of spatial-temporal lattice data.