Smooth Information Criterion for Regularized Estimation of Item Response Models

Abstract

Item response theory (IRT) models are frequently used to analyze multivariate categorical data from questionnaires or cognitive test data. In order to reduce the model complexity in item response models, regularized estimation is now widely applied, adding a nondifferentiable penalty function like the LASSO or the SCAD penalty to the log-likelihood function in the optimization function. In most applications, regularized estimation repeatedly estimates the IRT model on a grid of regularization parameters λ. The final model is selected for the parameter that minimizes the Akaike or Bayesian information criterion (AIC or BIC). In recent work, it has been proposed to directly minimize a smooth approximation of the AIC or the BIC for regularized estimation. This approach circumvents the repeated estimation of the IRT model. To this end, the computation time is substantially reduced. The adequacy of the new approach is demonstrated by three simulation studies focusing on regularized estimation for IRT models with differential item functioning, multidimensional IRT models with cross-loadings, and the mixed Rasch/two-parameter logistic IRT model. It was found from the simulation studies that the computationally less demanding direct optimization based on the smooth variants of AIC and BIC had comparable or improved performance compared to the ordinarily employed repeated regularized estimation based on AIC or BIC.