Abstract
The present paper introduces a new explanatory item response model to account for the learning that takes place during a psychometric test due to the repeated use of the operations involved in the items. The proposed model is an extension of the operation-specific learning model (Fischer and Formann in Appl Psychol Meas 6:397–416, 1982; Scheiblechner in Z für Exp Angew Psychol 19:476–506, 1972; Spada in Spada and Kempf (eds.) Structural models of thinking and learning, Huber, Bern, Germany, pp 227–262, 1977). The paper discusses special cases of the model, which, together with the general formulation, differ in the type of response in which the model states that learning occurs: (1) correct and incorrect responses equally (non-contingent learning); (2) correct responses only (contingent learning); and (3) correct and incorrect responses to a different extent (differential contingent learning). A Bayesian framework is adopted for model estimation and evaluation. A simulation study is conducted to examine the performance of the estimation and evaluation methods in recovering the true parameters and selecting the true model. Finally, an empirical study is presented to illustrate the applicability of the model to detect learning effects using real data.
Highlights
Learning effects may take place in educational and psychological testing when the items share a set of solution principles that can be extrapolated from one item to another, so examinees may learn to respond more effectively during the test
In order to study different conditions of misspecification, a 4 × 5 factorial design was used for the simulation study, resulting from the combination of generating models and fitted models
The simulation study illustrates the good performance of posterior predictive model checking (PPMC) for model evaluation and selection as well as the accuracy of the Markov chain Monte Carlo (MCMC) algorithm in recovering the true parameters from simulated data
Summary
Learning effects may take place in educational and psychological testing when the items share a set of solution principles that can be extrapolated from one item to another, so examinees may learn to respond more effectively during the test. There is a wide range of settings, both research and applied, where the detection and measurement of these learning effects may be of potential interest, such as those related to competence acquisition in developmental and educational contexts (e.g., Spada, 1977; Spada & McGaw, 1985) or to the substantive analysis of the learning processes that occur during a psychometric test (e.g., Lozano & Revuelta, 2020, 2021). The presence of learning effects during the test may involve meaningful item associations beyond those explained by conventional item response models. Incorporating previous practice into the models may allow for the detection and measurement of the learning effects as well as for the obtaining of unbiased estimates of item and person parameters while avoiding over-factoring
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