In our study, we focus on spatio-temporal causal auto-logistic model and proposed a two-step-centered parametrization version of it. We study the existence of the joint law according to the conditional marginals. The simulation study show that the one-step model can not reflect the temporal data structure when both spatial and temporal dependance are strong, while for the two-step model, there is an adequate agreement between the data structure and the temporal large-scale structure. The results of estimation for simulated lattices over years were performed by expectation-maximization (EM) pseudo-likelihood in two stages. They show that under the two-step centered parametrization, the inference for parameters of both temporal and spatial regressions are accurate, while under one-step centered parametrization their inference are always conflicting.