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, when reported, 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 relation between these correlation matrices,their analogues for covariances, along with the interpretation of the correlations they reportand the insights they can provide in understanding the relation of indicators with one another.The analogue of the REC matrix for covariances has the attractive property that its entries have an expected value of zero under a classical test theory model. The positive deviations of the REC matrix entries from zero help identify clusters of indicators that are more strongly related toone another, providing insights somewhat analogous tofactor analysis, but without the need for rotations or decisions concerning the number of factors.