An Innovative Approach for Modeling Crop Yield Response to Fertilizer Nutrients

Fertilizer recommendations seldom account for agro-climatic conditions, which are important factors that determine the response to fertilizer and the optimal rate of fertilizer. The nitrogen fertilizer response to open pollinated and hybrid canola types will also impact optimal nitrogen rates. This study used quantile regression to model canola yield response to nitrogen fertilizer. Quantile regression can apply different weights to the residuals, facilitating a response estimation where the agro-climatic conditions are not limiting and the yield response is due to the variable of interest. The economically optimal levels of fertilizers were calculated using the proposed and the conventional least squares procedures of the two canola types in western Canada. Results showed that the effects of nitrogen fertilizer on yield depended on the canola type and on the estimation procedure. Optimal levels of nitrogen for open-pollinated canola were estimated as 91, 115, and 134 kg ha-1 for severe, moderate and low levels of agro-climatic constraints. Hybrid had a higher yield potential, and also required more nitrogen fertilizer (137, 142, and 158 kg ha-1). Unlike conventional approach, proposed approach could benefit producer by recommending less (more) fertilizer when the crop response to fertilizer is expected to be low (high) due to agro-climatic conditions.Crop Production/Industries,

Nonlinear quantile mixed models

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is non-smooth as in the case of quantile regression. In this paper, we develop methods for the modeling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. This work represents an extension of the linear quantile mixed models of Geraci and Bottai (2014, Statistics and Computing). We develop a novel algorithm which is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. To assess the proposed methods, we present a simulation study and two applications, one in pharmacokinetics and one related to growth curve modeling in agriculture.Comment: 26 pages, 8 figures, 8 table

Piecewise-linear pathways to the optimal solution set in linear programming

This paper takes a fresh look at the application of quadratic penalty functions to linear programming. Recently, Madsen et al. (Ref. 1) described a continuation algorithm for linear programming based on smoothing a dual l1-formulation of a linear program with unit bounds. The present paper is prompted by the observation that this is equivalent to applying a quadratic penalty function to the dual of a linear program in standard canonical form, in the sense that both approaches generate continuous, piecewise-linear paths leading to the optimal solution set. These paths lead to new characterizations of optimal solutions in linear programming. An important product of this analysis is a finite penalty algorithm for linear programming closely related to the least-norm algorithm of Mangasarian (Ref. 2) and to the continuation algorithm of Madsen et al. (Ref. 1). The algorithm is implemented, and promising numerical results are given

bqror: An R package for Bayesian Quantile Regression in Ordinal Models

This article describes an R package bqror that estimates Bayesian quantile regression for ordinal models introduced in Rahman (2016). The paper classifies ordinal models into two types and offers computationally efficient, yet simple, Markov chain Monte Carlo (MCMC) algorithms for estimating ordinal quantile regression. The generic ordinal model with 3 or more outcomes (labeled ORI model) is estimated by a combination of Gibbs sampling and Metropolis-Hastings algorithm. Whereas an ordinal model with exactly 3 outcomes (labeled ORII model) is estimated using Gibbs sampling only. In line with the Bayesian literature, we suggest using marginal likelihood for comparing alternative quantile regression models and explain how to compute the same. The models and their estimation procedures are illustrated via multiple simulation studies and implemented in two applications. The article also describes several other functions contained within the bqror package, which are necessary for estimation, inference, and assessing model fit.Comment: 21 Pages, 4 figures, 2 Algorithm

Additive quantile regression for clustered data with an application to children's physical activity

Additive models are flexible regression tools that handle linear as well as nonlinear terms. The latter are typically modelled via smoothing splines. Additive mixed models extend additive models to include random terms when the data are sampled according to cluster designs (e.g., longitudinal). These models find applications in the study of phenomena like growth, certain disease mechanisms and energy consumption in humans, when repeated measurements are available. In this paper, we propose a novel additive mixed model for quantile regression. Our methods are motivated by an application to physical activity based on a dataset with more than half million accelerometer measurements in children of the UK Millennium Cohort Study. In a simulation study, we assess the proposed methods against existing alternatives.Comment: 50 pages, 4 figures, 2 tables (18 supplementary tables