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Abstract:
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As pointed out by Rencher (2004), the determinant of a covariance matrix is an index of generalized variance. That is, it quantifies data volume within a multivariate dataset. When standardized, it becomes the determinant ratio, an index of relative data volume adjusted for total variance. Using the assumption of equality of covariance, we examine the relationship between data volume and magnitude of covariance for various matrix sizes from a 4 x 4 matrix to a 20 x 20 matrix. By collectively comparing relative multicollinearity/sphericity across covariance matrices, one can ascertain the maximum number of variables to be used before one experiences diminishing returns, thus allowing researchers to determine at what point they can begin to throw variables out of their model. This will help ensure modeling efficiency by explaining the most variance with the least number of variables.
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