  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.
