Doubly ordered correspondence analysis: The effect of education on poverty by years

Correspondence analysis (CA) is a statistical technique used to analyze associations between categorical variables in a dataset, particularly useful for large contingency tables where relationships between rows and columns are not immediately apparent. This study explores the methodology and application of symmetrical doubly ordered correspondence analysis, which is applied when both variables in a contingency table are ordered. This research, a novel topic in Turkey, aims to understand the method fully and its application, including the use of bivariate moment decomposition. Another purpose of this study, in the application section of this method, is to investigate whether there is a relationship between the number of poor individuals and their education level over different years. The dataset comprises 66,158 individuals from Turkey, with rows representing educational levels (Illiterate, Literate with no diploma, Below high school, High school or its equivalent, and Higher education) and columns representing the years (2015-2023) that show the number of poor people. The data, sourced from the Turkish Statistical Institute (TÜİK), focuses on the period from 2015 to 2023. The poverty line is set at 50% of the median household disposable income. Statistical analysis was performed using R package version 4.3.2. This study applied symmetrical doubly ordered correspondence analysis, including the application of Bivariate Moment Decomposition for Pearson residuals and visualization of categorized variables. The result reveal a strong relationship between education levels and the number of poor people in different years. According to the findings, there is a notable trend in poverty levels from 2015 to 2023. Specifically, a decline in poverty is observed among individuals who are illiterate or possess literacy without a diploma. Conversely, an increase in poverty is evident among those who have attained a high school diploma or equivalent and higher educational levels. Individuals with education below high school show a relatively stable pattern with minimal fluctuations in the number of impoverished people over time. Keywords: Correspondence Analysis, Pearson Ratio, Orthogonal Polynomial, Ordered Categorical Variables, Bivariate Moment Decomposition, Poverty