## Quantile Approach to Contiguity Based Spatial Autocorrelation: Spatial Theta Lag And Conditional Weighting

Thesis Type: Doctorate

Institution Of The Thesis: Yildiz Technical University, Faculty Of Arts & Science, Department Of Statistics, Turkey

Approval Date: 2022

Thesis Language: English

Student: AHMET FURKAN EMREHAN

Supervisor: Doğan Yıldız

Abstract:

 Spatial Autocorrelation, whose tools detect whether data have a spatial attribution or not, is one of the central issues of Spatial Analysis. Data to be examined in Spatial Autocorrelation should be contiguity or distance based. The tools are developed to measure spatial Autocorrelation in the course of time: Moran’s I, Geary’s c, Getis-Ord G, and Joint-Count Statistics. Moran’s I is the most popular among these measures because it is easily interpretable and it is applicable to both contiguity and distance based data. To detect spatial autocorrelation Moran’s I is frequently used on contiguity-based data in the literature.Spatial units are linked to each other by means of contiguity or inverse distance matrix. The matrix determines the neighbourhood set. Moran’s I is based on the correlation between the observation of the spatial unit and its spatial Lag. The spatial Lag means the spatial effect, or more clearly, the effect of the neighbourhood set in this context. Spatial Lag is considered as the sum or weighted sum of the observations in the neighbourhood set. The mean of the neighbourhood set is widely used in the literature as a weighted sum thanks to the row-standardization of the contiguity matrix.The purpose of the dissertation is to use minimum, median and maximum of the observations of the neighbourhood set as a certain spatial lag at the detection of spatial effect. In doing so, the concepts of minimum, median and maximum are extended to quantiles of the neighbourhood sets. And the quantiles are modelled in a conceptual consistency as particular spatial lags by the help of a continuous function on [0,1] interval. Minimum, median and maximum are exceptional cases of quantiles. Thereby regardless of their sizes, the distributions of all neighbourhood sets are examined by means of quantiles and their particular spatial lags. Spatial theta lag denotes the spatial Lag based on quantiles. This approach creates a continuous index on [0,1] The conditional Contiguity Matrix is defined as the matrix to create Spatial Theta Lag.The effect of Spatial Theta Lag over Spatial Autocorrelation is examined employing Global ve Local Moran’s I as measure and Pseudo p, FDR, and Bonferroni Bound as statistical criteria, by dint of striking examples; Unhappiness Rate of People Aged 25-34 in 2013 and Voting Turnout in 2015 ,. Statistically significant clusters appeared in the mean based Spatial Autocorrelation are investigated in the light of minimum and maximum based spatial autocorrelation. The change of statistical significance levels of Spatial Theta Lag on [0,1] interval are shown. Finally, the suggestions are presented.