Correlation matrices (along with their unstandardized counterparts, covariance matrices) underlie the majority the statistical methods that researchers use today. A correlation matrix is more than a matrix filled with correlation coefficients. The value of one correlation in the matrix puts constraints on the values of the others, and the multivariate implications of this statement is a major theme of the volume. Alexandria Hadd and Joseph Lee Rodgers cover many features of correlations matrices including statistical hypothesis tests, their role in factor analysis and structural equation modeling, and graphical approaches. They illustrate the discussion with a wide range of lively examples including correlations between intelligence measured at different ages through adolescence; correlations between country characteristics such as public health expenditures, health life expectancy, and adult mortality; correlations between well-being and state-level vital statistics; correlations between the racial composition of cities and professional sports teams; and correlations between childbearing intentions and childbearing outcomes over the reproductive life course. This volume may be used effectively across a number of disciplines in both undergraduate and graduate statistics classrooms, and also in the research laboratory.

The Geometry of Correlation Matrices

The Geometry of Correlation Matrices

In the previous chapter, we described methods of graphing correlation matrices, as visualizing correlation matrices that are large or have a particular structure can provide more information for researchers or students than viewing the raw correlation matrix. In this chapter, we take the idea of visualizing correlation matrices further by discussing how to visualize the correlation space, which is a space that embeds correlation matrices within it. The material in this chapter may appear relatively abstract, and some of it is not highly relevant to the applied researcher. However, investigating the correlation space has led to recent discoveries regarding techniques involving correlation matrices, and learning about the correlation space can facilitate greater understanding of how correlation matrices are related ...

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