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Bayesian measurement error correction in structured additive distributional regression with an application to the analysis of sensor data on soil–plant variability
- Pollice, Alessio, Jona Lasinio, Giovanna, Rossi, Roberta, Amato, Mariana, Kneib, Thomas, Lang, Stefan
- Stochastic environmental research and risk assessment 2019 v.33 no.3 pp. 747-763
- Bayesian theory, Markov chain, agricultural management, alfalfa, forage, regression analysis, soil, Italy
- The flexibility of the Bayesian approach to account for covariates with measurement error is combined with semiparametric regression models. We consider a class of continuous, discrete and mixed univariate response distributions with potentially all parameters depending on a structured additive predictor. Markov chain Monte Carlo enables a modular and numerically efficient implementation of Bayesian measurement error correction based on the imputation of unobserved error-free covariate values. We allow for very general measurement errors, including correlated replicates with heterogeneous variances. The proposal is first assessed by a simulation trial, then it is applied to the assessment of a soil–plant relationship crucial for implementing efficient agricultural management practices. Observations on multi-depth soil information and forage ground-cover for a seven hectares Alfalfa stand in South Italy were obtained using sensors with very refined spatial resolution. Estimating a functional relation between ground-cover and soil with these data involves addressing issues linked to the spatial and temporal misalignment and the large data size. We propose a preliminary spatial aggregation on a lattice covering the field and subsequent analysis by a structured additive distributional regression model, accounting for measurement error in the soil covariate. Results are interpreted and commented in connection to possible Alfalfa management strategies.