Generalized method of moments approach for spatial-temporal binary data

Spatial-temporal models are progressively becoming an important method to assess public health data. The models with binary responses help to explain the spread of disease of over space and time by accounting for both spatial and temporal dependence among geographic locations. The centered spatial-temporal autologistic regression model accounts for binary data correlated across space and time. It uses logistic regression to model a response on explanatory variables and autoregression on responses from spatial neighborhoods. Statistical inference for the autologistic model has been based upon pseudo-likelihood, Monte Carlo Maximum Likelihood (MCML) or Bayesian hierarchical models. The added complexity of spatial and temporal dependence and associations between observations, as in health data, the likelihood based methods may not be the most efficient estimation techniques. They can have convergence issues and increase computation time, as the full conditional distribution needs to be defined. In this research, we develop an alternative to traditional likelihood methods using generalized method of moments. In this method the full distribution does not need to be specified, but rather can be specified by the first two moments. A set of estimating equations with a specified working correlation structure is constructed to deal with the spatial and temporal dependence of the data. This method is demonstrated and compared to MCML using the National Longitudinal Adolescent Health data to assess the effect of peer networks at multiple levels (friend, grade and school) on drug and alcohol use. Comparisons of convergence, computation time and parameter estimates are considered.