This paper introduces a quasi-deviance function for model selection of given spatial data. The proposed deviance function involves only the mean and covariance of responses, and therefore avoids the difficulty of specifying a full-likelihood function. We show that, under certain regularity conditions, the deviance function with quasi-likelihood estimating equation has a limiting chi-squared distribution. The asymptotic quadratic form of the deviance function provides a consistent method for selecting the true model. We also conduct simulations to evaluate the performance of the proposed method, and use the East Lansing Woods data to illustrate the application.
