Scale

Scale refers to the spatial domain of the study, it could be either small or large, depending on the study purpose. Explanatory models are scale-dependent, the result can be significantly different from the scale changing. Small scale study is reasonable to ignore larger-scale variability. 

Spatial autocorrelation

Spatial autocorrelation which refers to the non-random distribution of objects has a spatial dimension. Objects are spatially autocorrelated either by themselves or by the environment. Moran’s I am a weighted product-moment correlation coefficient, where the weights reflect geographic proximity. Values of I over 0 indicate positive spatial autocorrelation and vice versa. However, sometimes the natural data is hard to determine the spatial autocorrelation for its natural irregulations. Smoothing functions are difficult to deal with the naturally-occurring random fluctuations, thus, kriging, the semi-variogram geostatistical method is used to model the irregulated natural data. 

MAUP

Modifiable Areal Unit Problem (MAUP) is a source of statistical bias that is endemic to all spatially aggregated data. It could be impacted by both scale and aggregation. The scale effect is the tendency, for different statistical results to be obtained from the same set of data when the information is grouped to varying levels of spatial resolution. The aggregation effect is the variability in statistical results obtained within a set of modifiable units as a function of the various ways these units can be grouped at a given scale. The MAUP can be a political issue such as gerrymandering. So, how to divide the spatial units is essential for spatial analysis. Commonly, spatial units can be divided into natural and artificial types. However, other elements may also impact the aggregated data. Simpson’s paradox argues if the values of the variables vary in correlation with another, then, it may be impossible to obtain a reliable estimate of the accurate correlation between two variables, 

Neighbourhood models

The geographical areas are made up not of random groupings but tend to be more alike within the area than those outsides of the area. The three main classes of neighbourhood models are grouping models, in which similar individuals choose to locate in the same area; group-dependent models, in which individuals in the same area are subject to similar external influences; feedback models, in which individuals interact with each other and influence each other.