A multiclass logistic regression, Markov chain, and cellular automata integration for modelling urban land use change

Abstract

Cellular Automata (CA) models employ simple transition rules and neighbourhood interactions to determine cells' evolution. Integrating CA with other algorithms is often essential in order to obtain necessary statistical inferences. The integration of Binary Logistic Regression (BLR) and Markov chain (MC) with CA forms common CA integrations. For convenience, urban land use change is often modelled as a binary process (e,g. ‘undeveloped land’ and ‘developed land’), whereas in the real world urban land use change phenomenon could go beyond two processes (e. g. ‘undeveloped land’, ‘sparsely developed land’, ‘semi-highly developed land’, ‘highly developed land’, ‘very highly developed land’, etc.). The BLR-MC-CA hybrid model yields a binary outcome. In order to extend the BLR-MC-CA hybrid model to multivariate problems, we introduce a novel hybrid model, by simply replacing the BLR with the new Multiclass Logistic Regression (MLR) to obtain the new MLR-MC-CA hybrid model. Satellite remote sensing imageries acquired in 1984, 2000, and 2020 are used as input data. Four scenarios of urban land use change are modelled: ‘nonurban region’, ‘highest urban region’, ‘high urban region’, and ‘medium urban region’. These four scenarios are modelled with twelve urban land use drivers: distance to water body, distance to residential areas, distance to industrial and commercial areas, distance to major roads, distance to railway, distance to Lagos Island, distance to international seaport, distance to University of Lagos, income potential, population potential, distance to international airport, and distance to Lagos State University. Urban transitions 1984–2000 and 2000–2020 are used to simulate the urban states in 2000 and 2020 respectively; as well as to obtain the urban state in 2060. The validation of the experiment is largely based on McNemar's test and Receiver Operating Characteristics (ROC) curves. The results of the experiment indicate significant fit between the reference and the predicted data.