Family based spatial correlation model

Abstract

In spatial data analysis, linear, count or binary responses are collected from a large sequence of (spatial) locations. This type of responses from the (spatial) locations may be influenced by certain fixed covariates associated to the location itself as well as certain invisible random effects from the members of the neighboring locations. Also the responses may be subject to certain model errors. In familial/ clustered setup, responses are collected from the members of a large number of independent families, where the pairwise responses within the family are correlated. In a spatial set up, the pairwise responses within a family of locations are correlated similar to the familial setup, but unlike in the familial setup, the responses from neighboring families will also be correlated. In this thesis, unlike in the existing studies, we develop a moving or band correlation structure that reflects the correlations for within and between families. This is done first for linear (continuous) data and then for binary responses. As far as the inference are concerned, we discuss method of moments (MM) and maximum likelihood (ML) approach for the estimation of parameters in linear mixed model setup. Because the exact likelihood estimation approach for the spatial binary models is complicated, we demonstrate how to use the generalized quasi-likelihood ( GQL) approach for such models.