Spatial Autocorrelation Essay

The first law of geography states that “Everything is related to everything else but near things are more related than distant things” (Tobler, 1970 p236). In statistics, we call this phenomenon as spatial autocorrelation. In general sense, we can define the spatial autocorrelation as the extent to which objects or activities in the geographical proximity are related to other objects or activities on the surface of earth. In spatial analysis, we are dealing with information that is quite distinct. On one hand, we are taking into consideration the attributes of spatial aspects such as climate, altitude, temperature, road material, road surface conditions, drainage gullies, traffic load, curvature etc. but also the aspects that are location

In spatial autocorrelation, this assumption of independence is violated as error terms are correlated in space, the value of an error term is dependent on other error terms in its neighborhood i.e. they form a kind of patterns. The null hypothesis states that the values are randomly assigned to locations. We compute the test statistic and based on test statistic we either except or reject null hypothesis to check for spatial autocorrelation in our data (Plant 2012). If alternate hypothesis is excepted i.e. presence of spatial autocorrelation in our data then we must account for spatial dependence in our statistical analysis otherwise we might get biased or inaccurate results. The non-independence of outcomes represents a form of pseudo- replication and overestimates the available degrees of freedom (Dutilleul, 1993; Legendre etal.,2002). So statistical models may suffer incorrect parameter estimates and an underestimation of coefficient variances because of the impact of spatial autocorrelation (Anselin et al., 1998). To avoid getting inaccurate results or ill fit model we take into consideration spatial autocorrelation and find ways to account for it in the chosen model. When we are doing the analysis of spatial data, the correlation of observations is not unusual so ordinary regression models are not appropriate. (Carl and Kühn,

Since in classical statistics we do not consider locational information of the data that can be referenced through geographical co-ordinates, that is why the researchers were interested in spatial autocorrelation, as some of the information in classical statistics could not be captured resulting in value of estimators to be statistically insufficient (Griffith, 1992). A lot of research has been done in sectors such as political science, geography, medical science, ecology, environmental science etc. on the role of spatial autocorrelation and the effect it could have on the final results. Below we will discuss few papers that highlight the importance of spatial autocorrelation and the methods/models that they have adopted to account for spatial autocorrelation. Darmofal, (2009), paper on political event process highlights the importance of modelling spatial autocorrelation in political science data. The survival models that have been used in political science before, assume spatial independence. Political event process take place in both the dimensions i.e. space as well as time. To get valid statistics both space and temporal dimensions must be accounted for while shaping political event process. Hierarchical and individual frailty models have been used to examine the random effects and parametric Weibull and semiparametric Cox models have been used to