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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. While information granules of statistical independence of two variables can be viewed as determinants of 2times2-submatrices, those of three variables consist of several combinations of linear equations which will become residuals for odds ratio (outer products) when they are equal to 0. Interestingly, the...
This paper focuses on statistical independence of more than three variables from the viewpoint of linear algebra. While information granules of statistical independence of two variables can be viewed as determinants of 2 times 2- submatrices, those of three variables consist of several combination s of odds ratios, which can be viewed as a multivariate extension of determinants. Thus, in a more than...
This paper shows the meaning of Pearson residuals when a contingency table is three dimensional. While information granules of statistical independence of two variables can be viewed as determinants of 2 times 2- submatrices, those of three variables consist of several combinations of linear equations which will become odds ratio when they are equal to 0. Interstingly, the property on the symmetry...
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