Discretized and Aggregated: Modeling Dive Depth of Harbor Seals from Ordered Categorical Data with Temporal Autocorrelation

Ordered categorical data are pervasive in environmental and ecological data, and often arise from constraints that require discretizing a continuous variable into ordered categories. A great deal of data have been collected toward the study of marine mammal dive behavior using satellite depth recorders (SDRs), which often discretize a continuous variable such as depth. Additionally, data storage or transmission constraints may also necessitate the aggregation of data over time intervals of a specified length. The categorization and aggregation create a time series of ordered multicategory counts for each animal, which present challenges in terms of statistical modeling and practical interpretation. We describe an intuitive strategy for modeling such aggregated, ordered categorical data allowing for inference regarding the category probabilities and a measure of central tendency on the original scale of the data (e.g., meters), along with incorporation of temporal correlation and overdispersion. The strategy extends covariate-specific cutpoint models for ordinal data. We demonstrate the method in an analysis of SDR dive-depth data collected on harbor seals in Alaska. The primary goal of the analysis is to assess the relationship of covariates, such as time of day, with number of dives and maximum depth of dives. We also predict missing values and introduce novel graphical summaries of the data and results.