Exploring spatial vegetation dynamics using logistic regression and a multinomial logit model.
Abstract
This study presents statistical methodology that uses spatial explanatory variables to improve simpler estimates of transition probabilities from categorical data, such as vegetation type, that have been recorded as classified cells (pixels) in a grid or lattice at different times. A specific application is to examine successions in semi-natural vegetation in north-east Scotland. Questions related to these data include: Do transition probabilities of a pixel depend on the size of a patch of vegetation (polygon) and pixel location within the polygon? Do stable areas remain stable? Does the proximity of certain vegetation types influence transitions? We selected spatial variables that were likely to be important in this application, where short-range vegetative spread was thought to be an important factor. The multinomial logit model is used to estimate the transition probabilities as a function of explanatory variables, including location, neighbourhood information and other factors recorded at the start of the transition period. This model allowed the testing of different assumptions about the dynamics of underlying processes leading to transitions. When the number of categories, for example vegetation types, observed is large in comparison to the sample size, estimates of transition probabilities can be unreliable. We show that using change of category within the time period as the response in a logistic regression can still provide insight to the underlying dynamics of change in such a case. The methods are illustrated with some Scottish vegetation classification data with pixels of size 5×5 m covering a square of area 0.25 km2. Two contrasting squares were investigated: the first was upland moorland grazed by sheep and the second was a lowland area with more varied vegetation and low intensity grazing by cattle. In both squares there are strong spatial trends, and the neighbourhood of a pixel affected its transition. Prediction misclassification rates estimated from different models were compared using K-fold cross-validation. The multinomial model, including position in the square and number of neighbouring pixels in the same category as the pixel modelled, reduced the misclassification rate compared with the model without spatial explanatory variables. The improved estimates of transition probabilities could be incorporated into Markov models used in simulation studies to predict future vegetation changes under different management strategies.