Modeling for Dynamic Ordinal Regression Relationships: An Application to Estimating Maturity of Rockfish in California

Abstract: We develop a Bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models. A novel dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California.