Recategorization method based on dependence between qualitative variables using joint correspondence analysis with elliptical confidence regions

Abstract

Joint Correspondence Analysis (JCA) is a development method of Multiple Correspondence Analysis (MCA) that uses an algorithm to increase the percentage of variance. However, if the analysis used a large number of categories in qualitative data and there is no dependency, the analysis result in two dimensions may not be representative because the data variance is divided into several dimensions. Therefore, a recategorization method based on category dependencies is necessary to get a representative result. Elliptical confidence regions are the technique that can identify the contribution of dependence between two variables. Categories with insignificant contribution of dependencies are combined with other categories based on the shortest Euclidean distance. The novelty of this research is there is a stage of combining categories in correspondence analysis to reach a variance percentage of 70% in two dimensions. The study used data from the Environmental Quality Index (EQI) of Bandung Regency. The EQI consists of the Air Quality Index, the Water Quality Index, and the Land Cover Index. There are 8 characteristics with 37 categories and 31 districts used. According to the Chi-Square Test, 6 significant characteristics have a dependency on the district. Elliptical confidence regions were calculated six times based on simple correspondence analysis. There are differences treatment of characteristics and districts. The recategorization of characteristics is based on elliptical confidence regions, while districts were categorized based on Euclidean distance because the use of elliptical confidence regions generated six different results. The final two-dimensional map of JCA can explain 70.1% of the data variation in the 27th analysis with a total grouping of 5 districts and 17 categories.