Semiparametric Mixed Models for Increment-Averaged Data With Application to Carbon Sequestration in Agricultural Soils

Abstract

Adoption of conservation tillage practice in agriculture offers the potential to mitigate greenhouse gas emissions. Studies comparing conservation tillage methods to traditional tillage pair fields under the two management systems and obtain soil core samples from each treatment. Cores are divided into multiple increments, and matching increments from one or more cores are aggregated and analyzed for carbon stock. These data represent not the actual value at a specific depth, but rather the total or average over a depth increment. A semiparametric mixed model is developed for such increment-averaged data. The model uses parametric fixed effects to represent covariate effects, random effects to capture correlation within studies, and an integrated smooth function to describe effects of depth. The depth function is specified as an additive model, estimated with penalized splines using standard mixed model software. Smoothing parameters are automatically selected using restricted maximum likelihood. The methodology is applied to the problem of estimating a change in carbon stock due to a change in tillage practice.