Estimating equations for separable spatial-temporal binary data

For binary data with correlation across space and over time, the literature concerning the estimation of fixed effects in marginal models is limited. In this paper, we model the marginal probability of binary responses in terms of parameters of interest by a logistic function. An estimating equation based on the quasi-likelihood concept is developed to estimate parameters. Under separable correlation models, we show that the quasi-likelihood estimate is asymptotically optimal. A series of simulations is conducted to evaluate how the efficiency varies with the regression coefficients. We also compare the relative efficiency with another estimating equation by simulations. The proposed method is applied to an ecological study of forest decline to test independence of two spatial-temporal binary outcomes.