Psychometrical Modeling of Components of Composite Constructs: Recycling Data Can Be Useful
This paper describes a list of studies necessary to justify the simultaneous use of both the overall test score and the subscale scores when measuring complex constructs. We investigate in detail one of the strategies for modeling composite constructs, which is popular within the international comparative studies of education. This strategy is based on repetitive recalibrations of the same data using unidimensional models for reporting overall test score and multidimensional models for reporting its components. We use Monte-Carlo simulations to illustrate that repetitive recalibrations of the data using unidimensional and multidimensional models yield, basically, the same results after their transformation to the same scales. However, we also illustrate that the fit of the unidimensional models to the data may be confounded if the components of the composite vary in terms of their relations with each other and their variance. We illustrate the studied strategy for modeling composite constructs using the computer adaptive test PROGRESS-ML, which measures basic math literacy in the third grade.