A Hamiltonian-Gibbs Bayesian Sampler with Monotonicity Constraints for Restricted Latent Class Models

Abstract: In this talk, a novel Bayesian algorithm with monotonicity constraints for restricted latent class models (RLCMs) is introduced. RLCMs are a family of generalized latent variable models that model individuals’ cognitive or psychological states based on their response patterns to a set of observed indicator variables (e.g., surveys, educational assessments, psychological inventories). The proposed algorithm integrates Gibbs sampling – a popular Markov Chain Monte Carlo technique – with Hamiltonian dynamics – a technique that originated in the physics literature for modeling the movement of a particle in a physical system. The Hamiltonian step of the algorithm is embedded with a “bounce-and-reflect” scheme that enforces monotonicity constraints on the model parameters and ensures the latent classes don’t “label switch” during estimation. We show that Gibbs sampling and Hamiltonian dynamics can be combined to create an efficient estimation algorithm for RLCMs. The theoretical and computational properties of the algorithm are explored through comprehensive Monte Carlo simulation studies and is applied to a real dataset of clinical patient’s responses to a mental health assessment. Results from the simulation studies indicate that the algorithm is capable of providing accurate parameter estimates within a few hundred iterations in well-designed assessments.