Regularized Generalized Logistic Item Response Model

Item response theory (IRT) models are factor models for dichotomous or polytomous variables (i.e., item responses). The symmetric logistic or probit link functions are most frequently utilized for modeling dichotomous or polytomous items. In this article, we propose an IRT model for dichotomous and polytomous items using the asymmetric generalistic logistic link function that covers a lot of symmetric and asymmetric link functions. Compared to IRT modeling based on the logistic or probit link function, the generalized logistic link function additionally estimates two parameters related to the asymmetry of the link function. To stabilize the estimation of item-specific asymmetry parameters, regularized estimation is employed. The usefulness of the proposed model is illustrated through simulations and empirical examples for dichotomous and polytomous item responses.