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The authors formulate a dynamical non-compensatory multidimensional item response theory (MIRT) model that couples a linear dynamical state-space process with non-compensatory item response likelihoods to trace continuous multi-skill growth over time. While existing dynamic evaluation models rely on compensatory assumptions where strength in one latent skill offsets deficits in another, this inductive bias produces severe misestimation on tasks requiring conjunctive mastery of multiple capabilities. Inferring latent trajectories via a variational Gaussian approximation within a Monte Carlo Expectation-Maximization framework, the model eliminates the systematic underestimation errors typical of standard compensatory baselines.
Assuming that latent capabilities can compensate for one another causes severe underestimation bias when evaluating dynamic multidimensional skill trajectories on complex, multi-prerequisite tasks.
Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback–Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.