Maximal Reliability and Composite Reliability: Examining Their Difference for Multicomponent Measuring Instruments Using Latent Variable Modeling

A latent variable modeling method for examining the difference between maximal reliability and composite reliability for homogenous multicomponent measuring instruments is outlined. The procedure allows point and interval estimation of the discrepancy between the reliability coefficients associated with the optimal linear combination and with the popular unit-weighted sum of the scale components. The approach permits a researcher to make an informed choice if needed between the maximal reliability and composite reliability coefficients and concepts in an empirical setting as indexes of quality of measurement with an instrument under consideration. The discussed method is illustrated using numerical data.