Use of mixed effect models to investigate the relationships of hyperspectral and fluorescence data with plant variables

Proximal sensors, such as hyperspectral and fluorescence devices, provide important information about plant status as they enable field investigation in real time and at very fine spatial and temporal scales. Statistical analysis is fundamental to extract critical features and assess relationships between proximal indices and plant variables. In modelling such relationships, spatial autocorrelation of residuals should be taken into account as it can affect estimates of model coefficients and inference from statistical models. The aim of this study was to compare spatial and non-spatial (OLS) models for quantifying predictive relationships between proximal data (hyperspectral and fluorescence) and plant variables (N.uptake and LAI). Proximal and biometric data were collected in a field located in Foggia (southern Italy), at anthesis stageof durum wheat in 2014, on 104 georeferenced locations. Fluorescence data were collected using a portable fluorimeter (Multiplex). Measured variables (fluorescence emitted in yellow, red and far-red induced by UV, blue, green and red light) were synthetized by factor analysis and the first two extracted components (F1, F2) were used in this study. Hyperspectral signatures were recorded using a sensor operating in the 325-1075nm region (Fieldspec, ASD) and were collected only in 52 locations, at about 50cm above the canopy. Data were processed by computing: discrete vegetation indices; multivariate indices using the whole spectrum; indices based on the shape of reflectance curve. Mixed-effects models with correlated errors were estimated between plant variables and sensing data. Nonspatial models, including same fixed effects of spatial models but assuming independence of errors, were also computed. Residual autocorrelation was evaluated through Moran test; spatial and non-spatial models were compared using log likelihood ratio. Moran test and log ratio showed that residuals were not spatially correlated for regressions between hyperspectral indices and plant variables; this result might be attributed to the too coarse sampling scale. Significant spatial dependence was instead observed for fluorescence variables, particularly for the relationship between F1 and N.uptake (Moran test, P=0.0016; log ratio, P=0.055). Spatial models taking into account residual autocorrelation can be very helpful in agricultural and environmental research as they allow correct estimation of confidence intervals and hypothesis testing