The exploratory Generalized Noisy Inputs, Deterministic “OR” gate model: A duality proof and application

Abstract

Cognitive diagnosis models (CDMs) are useful methods for classifying individuals into substantively meaningful latent classes. Recent research applied disjunctive models to psychopathology questionnaires to support clinical diagnoses. We discuss a more general disjunctive model than used in previous research, the Generalized, Noisy Inputs, Deterministic "OR'' Gate (GNIDO) model. We generalize the proof of Köhn & Chiu (2016) to establish the duality between the GNIDO and the Generalized, Noisy Inputs, Deterministic "AND'' Gate (GNIDA) model, which is also known as the reduced reparameterized unified model (rRUM). We apply an exploratory GNIDO model to 14 anxiety items from the Wisconsin Longitudinal Study to uncover the latent structure. Our application of the exploratory GNIDO demonstrates the clinical value in using exploratory CDMs in applied research. We discuss the implication of our results for future methodological research as well as substantive efforts that aim to use clinical diagnoses to transition patients to symptom-free classes with more targeted interventions.