Methodology adjusting for least squares regression slope in the application of multiplicative scatter correction to near‐infrared spectra of forage feed samples

Abstract

Scatter corrections are commonly applied to refine near‐infrared (NIR) spectra. The aim of this study is to assess the impact of measurement errors when using ordinary least squares (OLS) for multiplicative scatter correction (MSC). Any measurement errors attached to the set‐mean spectrum may attenuate the OLS slope and that in turn will affect the estimate of the intercept and the adjustment of the spectra when using MSC methods to mitigate scattering. A corrected least squares slope may be used instead to prevent this problem, although the impact of this approach on the final outcome will depend on the relative size of the measurement errors in the individual spectra and the set‐mean spectrum. The errors‐in‐variables or type II regression model (also known as Deming regression) and its special cases, major axis (MA) and reduced major axis (RMA), are discussed and illustrated. The extent of OLS slope bias or attenuation is demonstrated as is the resulting MSC spectral distortion. Further modification to the MSC transformation method is also suggested. The influence of scattering correction (by MSC, standard normal variate (SNV) and detrending) and of using the maximum likelihood estimate of the slope for MSC on the prediction of chemical composition of Lucerne herbage from NIR spectra was assessed. The predictive performance was slightly improved by the use of scattering corrections with fairly minor differences among methods. Nonetheless, it seems well worth considering the use of type II regression models for assessing MSC application aiming at improving the goodness of prediction from NIR spectra.

A Bayesian model‐based reduced major axis regression

“…However, this assumption may be violated since the independent measurements may also suffer from measurement error (Harper, 2014). To deal with measurement errors in both the dependent and independent variables, errors‐in‐variable (EIV) modeling approaches are proposed (Dhanoa et al., 2023; Geraci, 2018). One important approach in the EIV regression framework is the reduced major axis (RMA) regression, which is also named as the geometric mean regression (Smith, 2009; Teissier, 1948).…”