New measurement models can be generated through the combination of psychometrics and cognitive psychology. Following a test, these models permit the creation of student portraits in relation to specific cognitive abilities. This paper presents a comparative examination of five models that link both psychometric and cognitive views. Comparisons are made in several areas, including the validity and reliability of the models, as well as how interpretable the results are, how the quality of the attributes is studied a priori, and how students are characterized.