The unilateral spatial autogressive process for the regular lattice two-dimensional spatial discrete data

Identifier:  RP:4690

Handle: https://hdl.handle.net/20.500.11797/RP4690

Authors:  Jowaheer, Vandna; Khan, Naushad Mamode; Karlis, Dimitris; Chutoo, Azmi

Abstract:
This paper proposes a generalized framework to analyze spatial count data under a unilateral regular lattice structure based on thinning type models. We start from the simple spatial integer-valued auto-regressive model of order 1. We extend this model in certain directions. First, we consider various distributions as choices for the innovation distribution to allow for additional overdispersion. Second, we allow for use of covariate information, leading to a non-stationary model. Finally, we derive and use other models related to this simple one by considering simplification on the existing model. Inference is based on conditional maximum likelihood approach. We provide simulation results under different scenarios to understand the behaviour of the conditional maximum likelihood. A real data application is also provided. Remarks on how the results extend to other families of models are also given.