Novel Psychometric Indicator Assessments: The Relative Excess Correlation and Associated Matrices

For a series of indicators used to assess psychosocial constructs, we propose reporting new types of correlation matrices to gain greater insight into the relation of the indicators with one another. What we define as the observed residual correlation (ORC) matrix can give insight as to whether, when a given indicator is above the indicator-average scores across all indicators for that individual, what other indicators might be anticipated to be above that individual's average score as well. What we define as the relative excess correlation (REC) matrix can give insight, for each pair of indicators, whether the strength of that particular correlation is above or below what might have been anticipated based on the correlation of each of those two indicators with all of the others. The ORC and REC matrices will, generally, have numerous negative entries even if all of the raw correlations between each pair of indicators are positive. We discuss the properties of, and the relations between, these correlation matrices, and their analogues for covariances. The positive deviations of the REC matrix entries from zero also can help identify clusters of indicators that are more strongly related to one another, providing insights somewhat analogous to factor analysis, but without the need for decisions concerning rotations or the number of factors. However, the ORC and REC matrices can also be used purely descriptively to provide insights into understanding the relation of indicators with one another.