Split‐plot regression models with both design and spectroscopic variables

The main object of this work is to compare two methods for combining spectroscopic measurements and design variables in a regression model, when the data has a split‐plot error structure. Focus of the comparison is on prediction ability and interpretation. The need for such regression models is present in many production processes, since the end‐product quality usually is affected by both raw material quality and processing. If the raw materials are complex, biological substances, it is often natural to characterise them by spectroscopic measurements. This paper presents a case from the fish feed industry, where a designed experiment was carried out to investigate if quality variations in a certain raw material affect the end product. It was not known which raw material properties that are important, and NIR spectroscopy was therefore used for characterisation. Recipe and process settings were also varied. Practical considerations imposed restrictions on the randomisation, and this led to a split‐plot design. The regression model was estimated by restricted maximum likelihood (REML), to account for the split‐plot structure. The two methods presented here combine design variables with either PCA or PLS on the spectra. We call the methods REML‐PCA and REML‐PLS. In this case, both methods perform equally well regarding model fit and prediction ability. However, REML‐PLS is easier to interpret as less components are needed and the components are directly connected to the response.