Some Properties of the Scaled Burt Matrix on Multiple Correspondence Analysis

Udjianna Sekteria Pasaribu, Karunia Eka Lestari, Sapto Wahyu Indratno, Hanni Garminia, R. R. Kurnia Novita Sari


Multiple correspondence analysis (MCA) is well-known in statistics as a data analysis technique for multiple categorical variables. This method detects and represents underlying structures in a data set by representing data as points in a low-dimensional space. MCA is performed by applying the simple correspondence analysis (CA) algorithm to either an indicator matrix or a Burt matrix formed from these variables. Furthermore, the Burt matrix is scaled and undertaken eigendecomposition to get coordinates, which depicts the association's nature among variables. This study re-proposed the scale matrix of the Burt matrix, whose elements are the scale values of the categories of a variable, then so-called the scaled Burt matrix. While some researchers are interested in many MCA applications, we convenient our attention to exploring the properties of the scaled Burt matrix from a matrix algebraic perspective. These properties are derived mathematically to investigate the link between the Burt matrix and its scale matrix in representing the variables' associations.



Keywords: Burt matrix, categorical data analysis, indicator matrix, multiple correspondence analysis, scale matrix.



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