Parsimonious item response theory modeling with different link functions

[EMBARGOED UNTIL 6/1/2023] Traditional item response theory (IRT) models assume a symmetric error distribution and rely on symmetric (logit or probit) link functions to model the response probabilities. However, this assumption does not always hold in item response data. To explore the possible benefits of alternate link functions, I developed and investigated a set of one-parameter IRT models for unidimensional tests with dichotomous items by specifying the complementary log-log (CLL), negative log-log model (NLL), and cauchit links. In a series of simulations studies, I demonstrated that these parametrically parsimonious alternate-link IRT models are comparable to traditional IRT models with regard to (1) data distribution shape, (b) inflection point shift, (c) structural similarities, and (d) response behaviors. Importantly, these four properties provide a rationale for how certain parametrically simple alternate-link models can outperform more parametrically complex traditional IRT models. Specifically, I demonstrate that the CLL model accounts for the effect of guessing because it has an item characteristic curve with a higher inflection point than that of the traditional Rasch or two-parameter logistic (2PL) models. Similarly, the NLL model addresses the effects of slipping via an inflection point that is lower than in the Rasch or 2PL models. Importantly, unlike traditional IRT models that focus on guessing and slipping as response behaviors associated with the extreme levels of the latent trait, I show that the CLL and NLL models assume such behaviors affect responses across the entire range of the trait. I also present the cauchit model, which treats both guessing and slipping effects as outliers. The simulation results reveal that these one-parameter alternate-IRT models are robust to small sample sizes (e.g., N = 100), and facilitate item-weighted scoring. I then provide further evidence for these claims by applying the CLL, NLL, and cauchit models to empirical data. Finally, I propose some extensions of alternate-link IRT modeling beyond the particular (unidimensional dichotomous) context that formed the basis of my simulations and empirical analysis. I conclude by discussing the implications of this work for applied measurement and psychometric research.