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.

Methods for Correlation/Covariance Matrices as the Input Data

Methods for Correlation/Covariance Matrices as the Input Data

In this chapter, we treat the correlation matrix not as a descriptive tool of the raw data, but rather as the input data to be directly analyzed. We introduce statistical methods that are commonly employed in the social sciences for correlation matrices. These methods often fall into the category of statistical modeling, a broad methodological perspective that includes hypothesis testing as a special case (e.g., Rodgers, 2010). Many modern statistical modeling methods exist that treat correlations as input data, including path analysis, structural equation modeling (SEM), factor analysis, components analysis, multilevel modeling, and latent growth curve modeling, among others.

In this introduction to this chapter, we present some brief comments about models and about correlation matrices. However, ...