Optimal Linear Combinations From Multidimensional Behavioral Measuring Instruments: Can We Obtain the Best From the Whole and From Its Parts?

A covariance structure analysis procedure is outlined that can be used for estimating optimal linear combinations of the components of behavioral scales measuring two or more underlying dimensions evaluated by corresponding subscales. The method provides a set of optimal weights for the linear combination of all scale components that possesses highest reliability, and a set of such weights with respect to each subscale. The approach is relevant when for validity and construct representation reasons researchers decide to use complex structure measuring instruments and are substantively interested in subject performance on the overall scale as well as on each of the subscales. The procedure is readily applied with freely available software and is illustrated on multidimensional scale data.