Geographically weighted discriminant analysis: An Application on election results

Discriminant Analysis (DA) is a broad statistical term used to examine relationships between multiple variables. This analysis uses a linear combination of independent variables to predict membership of a target group. Research in this area has developed and expanded since Fisher's initial work in 1936. The focus of this thesis is to introduce Geographically Weighted Discriminant Analysis (GWDA). The main purpose of GWDA is to find the discriminant functions that distinguish different groups from each other, and with the help of these functions, to reveal the discriminant variables that have the most effect on the separation between groups. GWDA is an extended approach by adding geographical variables to discriminant analysis. This method takes into account the more effective separation of groups in the analysis of geographical data sets and the greater weight of geographical features in classification. The potential and practical applications of DA and GWDA methods in geographical data analysis are investigated in this study, aiming to make a new contribution to the existing literature. In this GWDA-oriented work, Geographically Weighted Descriptive Statistics (GWSS) will also be introduced. In this context, it will also focus on a different perspective beyond ordinary descriptive statistics. These geographically weighted statistics are based on spatial heterogeneity or geographical heterogeneity. In the application study, various factors affecting voter behaviour will be analysed. Data from the results of the second presidential election held on 28 May 2023 in 81 provinces in Turkey were used. The factors used for analysis are as follows: urbanisation rate, primary school graduation rate, high school graduation rate, high school graduation rate, faculty graduation rate, master's degree graduation rate, young age rate, middle age rate, old age rate, unemployment rate, illiteracy rate, presidential election female voter rate and logarithmic GDP per capita. These factors were used in the process of analysing the election results with DA and GWDA. GWDA analyses the spatial differences of the factors affecting the election results. It reveals the effects of local characteristics by making separate calculations at each observation point. Moreover, GWDA provides an understanding of regional dynamics and factors by analysing the differences between regions in detail. According to the findings of the empirical analyses, GWDA provides stronger results than DA. Important clues have been obtained for the socio-economic and demographic factors affecting the presidential election results in Turkey. Keywords: Discriminant Analysis, Geographically Weighted Summary Statistics, Geographically Weighted Discriminant Analysis, Presidential Elections