Understanding correlation matrices

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Bibliographic Information

Understanding correlation matrices

Alexandria Hadd, Joseph Lee Rodgers

(Sage publications series, . Quantitative applications in the social sciences ; v. 186)

Sage, c2021

Available at  / 10 libraries

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Note

Includes bibliographical references (p. 105-111) and index

Description and Table of Contents

Description

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.

Table of Contents

Series Editors Introduction Preface Acknowledgments About the Authors Chapter 1: Introduction The Correlation Coefficient: A Conceptual Introduction The Covariance The Correlation Coefficient and Linear Algebra: Brief Histories Examples of Correlation Matrices Summary Chapter 2: The Mathematics of Correlation Matrices Requirements of Correlation Matrices Eigenvalues of a Correlation Matrix Pseudo-Correlation Matrices and Positive Definite Matrices Smoothing Techniques Restriction of Correlation Ranges in the Matrix The Inverse of a Correlation Matrix The Determinant of a Correlation Matrix Examples Summary Chapter 3: Statistical Hypothesis Testing on Correlation Matrices Hypotheses About Correlations in a Single Correlation Matrix Hypotheses About Two or More Correlation Matrices Testing for Linear Trend of Eigenvalues Summary Chapter 4: Methods for Correlation/Covariance Matrices as the Input Data Factor Analysis Structural Equation Modeling Meta-Analysis of Correlation Matrices Summary Chapter 5: Graphing Correlation Matrices Graphing Correlations Graphing Correlation Matrices Summary Chapter 6: The Geometry of Correlation Matrices What Is Correlation Space? The 3 x 3 Correlation Space Properties of Correlation Space: The Shape and Size Uses of Correlation Space Example Using 3 x 3 and 4 x 4 Correlation Space Summary Chapter 7: Conclusion References Index

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