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This paper focuses on residual analysis of statistical independence of multiple variables from the viewpoint of linear algebra. The results show that multidimensional residuals are represented as linear sum of determinants of 2 × 2 submatrices, which can be viewed as information granules measuring the degree of statistical dependence.
This paper shows the meaning of Pearson residuals as an indicator of statistical independence in a multi-way contingency table. While information granules of statistical independence of two variables can be viewed as determinants of 2 ?? 2- submatrices, those of multivariate cases consist of linear sum of residuals for odds ratios, which can be viewed as an extention of determinants in 2 ?? 2 matrices.
This paper focuses on statistical independence of multiple variables from the viewpoint of linear algebra. The residual for odds ratio, which can be viewed as an extension of the determinant of two dimensional contingency matrix, plays an important role in decomposition of multivariate data tables.
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