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 that arise from estimation of cut-off points relating the latent continuous and ordinal responses. 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. Supplementary materials for this article are available online.

KEYWORDS:

• Chilipepper rockfish
• Dependent Dirichlet process
• Dynamic density estimation
• Growth curves
• Ordinal regression

Acknowledgments

The authors thank Stephan Munch for providing the rockfish data and for several useful comments on the interpretation of the results, Alec MacCall, Don Pearson, and Marc Mangel for valuable input on data collection and on key aspects of the specific problem from fisheries research, as well as an associate editor and two reviewers for several comments that greatly improved the presentation of the material in the article.

Additional information

Funding

This research is part of the Ph.D dissertation of M. DeYoreo, completed at University of California, Santa Cruz, and was supported in part by the National Science Foundation under award DMS 1310438.