Regularization methods for item response and paired comparison models

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A key aspect of psychometric modeling is measuring latent traits. This dissertation examines two widely used methods for analyzing these traits: item response methods and paired comparisons. Traditional models, such as the Rasch model for item response data and the Bradley-Terry model for paired comparisons, do not incorporate covariate information. This work addresses the integration of various types of covariates into both item response and paired comparison models. While this inclusion enhances model flexibility, it also increases complexity. Regularization methods are presented as effective tools to manage the growing number of parameters, helping to distinguish between essential and superfluous ones. The proposed methodologies are demonstrated through a series of simulations and real data applications, showcasing their practical utility and relevance in the field.