MSc Defence: POGEE: Penalized Ordinal Generalized Estimating Equations With Application to Optimal Soil Nitrate Sampling Timing in Corn Production (Jenelle Barker)

CANDIDATE: Jenelle Barker

ABSTRACT: High-dimensional ordinal longitudinal data arise in many applications. For example, corn farmers typically use nitrogen fertilizer to increase their yield production. Nevertheless, identifying the optimal time during the growing season to test the soil nitrogen levels and derive the amount of nitrogen to be applied can be framed as an ordinal regression problem. This is because the soil nitrogen testing timing is an ordinal response (categories are the stages of growth timings), and the soil, climate, landscape and farm characteristics form the set of predictors. However, observations taken at different locations within a farm, or in the same growing season across years, are correlated. Unfortunately, methods for ordinal regression rarely combine variable selection with within-cluster dependence. This thesis proposes POGEE, a penalized ordinal regression based on generalized estimating equations. In linear effect simulations, POGEE showed strong predictor recovery, lower coefficient-estimation error, and greater feasibility as dimensionality increased compared to existing ordinal regression methods. On the other hand, performance weakened under nonlinear misspecification, and the row-column correlation association structure was unstable in small samples. A real-world analysis of soil nitrate testing timing for corn in Ontario, based on weather and field characteristics, showed that sampling at later stages of crop growth was most frequently optimal, with soil moisture, temperature, radiation, and soil characteristics most associated with timing. Overall, POGEE provides an interpretable option for high-dimensional clustered ordinal data, but further work is needed to improve its convergence and predictive performance.