Estimation in autoregressive population models

Autoregressive (AR) models for spatial and social interaction have been proposed by many authors. A sample of units is obtained and the model is applied to this sample. Estimation methods such as the maximum likelihood method (ML) have been employed and investigated in the literature. The main assumption is that a response depends on other responses, when these units interact. Some of those units will be in the sample and some in the non-sample. Therefore the model should apply to the whole population rather to the sample only. Under such a population model, the marginal model for the responses of the sample is generally not of the same form and depends on covariates and interactions of non-sample units. Standard estimation methods using the sample information only are inappropriate. In this paper we investigate the performance of the standard ML method and a modified ML version that is based on the population model. Due to the population size, we also consider an approximate ML method. The results show that the standard ML method yields biased estimates and the modified ML version along with the approximate method perform far better.