A new centered spatio-temporal autologistic regression model. Application to spatio-temporal analysis of esca disease in a vineyard

Abstract: We propose a new centered autologistic spatio-temporal model for binary data on a lattice. The centering allows the interpretation of the autoregression coefficients in separating the large scale structure of the model corresponding to an expected mean and the small-scale structure corresponding to the auto-correlation. We discuss the existence of the joint law of the process and show by simulation the interest of this kind of centering. We propose and show the efficiency of the maximum pseudo-likelihood estimator and also a method to choose the best structure of neighborhood. Method is applied to model and fit epidemiological data about Esca disease on a vineyard of the Bordeaux region.