Variable Family Size Based Spatial Moving Correlations Model

It is well known that the autocorrelations among responses play a significant role in time series setup mainly for the purpose of forecasting. Similarly, in a spatial setup, spatial variation and correlations among responses collected from a large sequence of spatial locations are important parameters for any practical inferences. For example, variation in plant crop damages and correlations among neighboring plant crop damages are important parameters to understand before one can take suitable measure to prevent such damages in the future. In this setup, a group of neighboring plants or locations constitute a family, and the pairwise responses within a family of locations are likely to be correlated. Furthermore, the responses from neighboring families will also be correlated but they become uncorrelated when the locations are far apart. In this paper, we deal with modeling of spatial correlations for continuous data collected from non-linear sequence of locations and propose a pairwise linear mixed models-based moving or band correlation structure that reflects the correlations for within and between families. The proposed correlation structure is then exploited to develop the likelihood inferences for both variance and correlation parameters of the model. The regression parameters are also estimated. The correlation model and the inferences are illustrated using a monte carlo study for a simpler case with responses collected from a linear sequence of locations. The correlation mis-specification effects are also discussed.