Modelling land use change with generalized linear models--a multi-model analysis of change between 1860 and 2000 in Gallatin Valley, Montana.

This paper develops an approach to modelling land use change that links model selection and multi-model inference with empirical models and GIS. Land use change is frequently studied, and understanding gained, through a process of modelling that is an empirical analysis of documented changes in land cover or land use patterns. The approach here is based on analysis and comparison of multiple models of land use patterns using model selection and multi-model inference. The approach is illustrated with a case study of rural housing as it has developed for part of Gallatin County, Montana, USA. A GIS contains the location of rural housing on a yearly basis from 1860 to 2000. The database also documents a variety of environmental and socio-economic conditions. A general model of settlement development describes the evolution of drivers of land use change and their impacts in the region. This model is used to develop a series of different models reflecting drivers of change at different periods in the history of the study area. These period specific models represent a series of multiple working hypotheses describing (a) the effects of spatial variables as a representation of social, economic and environmental drivers of land use change, and (b) temporal changes in the effects of the spatial variables as the drivers of change evolve over time. Logistic regression is used to calibrate and interpret these models and the models are then compared and evaluated with model selection techniques. Results show that different models are 'best' for the different periods. The different models for different periods demonstrate that models are not invariant over time which presents challenges for validation and testing of empirical models. The research demonstrates (i) model selection as a mechanism for rating among many plausible models that describe land cover or land use patterns, (ii) inference from a set of models rather than from a single model, (iii) that models can be developed based on hypothesised relationships based on consideration of underlying and proximate causes of change, and (iv) that models are not invariant over time.