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Item response theory aims to estimate respondent's latent skills from theirresponses in tests composed of items with different levels of difficulty.Several models of item response theory have been proposed for different typesof tasks, such as binary or probabilistic responses, response time, multipleresponses, among others. In this paper, we propose a new version of$\beta^3$-IRT, called $\beta^{4}$-IRT, which uses the gradient descent methodto estimate the model parameters. In $\beta^3$-IRT, abilities and difficultiesare bounded, thus we employ link functions in order to turn $\beta^{4}$-IRTinto an unconstrained gradient descent process. The original $\beta^3$-IRT hada symmetry problem, meaning that, if an item was initialised with adiscrimination value with the wrong sign, e.g. negative when the actualdiscrimination should be positive, the fitting process could be unable torecover the correct discrimination and difficulty values for the item. In orderto tackle this limitation, we modelled the discrimination parameter as theproduct of two new parameters, one corresponding to the sign and the secondassociated to the magnitude. We also proposed sensible priors for allparameters. We performed experiments to compare $\beta^{4}$-IRT and$\beta^3$-IRT regarding parameter recovery and our new version outperformed theoriginal $\beta^3$-IRT. Finally, we made $\beta^{4}$-IRT publicly available asa Python package, along with the implementation of $\beta^3$-IRT used in ourexperiments.

$\beta^{4}$-IRT: A New $\beta^{3}$-IRT with Enhanced Discrimination Estimation