The aim of the current study is to present three assumptions common to psychometric theory and psychometric practice, and to show how alternatives to traditional psychometrical approaches can be used to improve psychological measurement. These alternatives are developed by adapting each of these three assumptions. The assumption of structural validity relates to the implementation of mathematical models. The process assumption which is underlying process generates the observed data. The construct assumption implies that the observed data on its own do not constitute a measurement, but the latent variable that originates the observed data. Nonparametric item response modeling and cognitive psychometric modeling are presented as alternatives for relaxing the first two assumptions, respectively. Network psychometrics is the alternative for relaxing the third assumption. Final remarks sum up the most important conclusions of the study.

Nonparametric procedures are used to add flexibility to models. Three nonparametric item response models have been proposed, but not directly compared: the Kernel smoothing (KS-IRT); the Davidian-Curve (DC-IRT); and the Bayesian semiparametric Rasch model (SP-Rasch). The main aim of the present study is to compare the performance of these procedures in recovering simulated true scores, using sum scores as benchmarks. The secondary aim is to compare their performances in terms of practical equivalence with real data. Overall, the results show that, apart from the DC-IRT, which is the model that performs the worse, all the other models give results quite similar to those when sum scores are used. These results are followed by a discussion with practical implications and recommendations for future studies.