Parsimonious Bayesian factor analysis for modelling latent structures in spectroscopy data

In recent years, within the dairy sector, animal diet and management practices have been receiving increased attention, in particular, examining the impact of pasture-based feeding strategies on the composition and quality of milk and dairy products in line with the prevalence of premium grass-fed dairy products appearing on market shelves. To date, methods to thoroughly investigate the more relevant differences induced by the diet on milk chemical features are limited; enhanced statistical tools exploring these differences are required. Infrared spectroscopy techniques are widely used to collect data on milk samples and to predict milk related traits and characteristics. While these data are routinely used to predict the composition of the macro components of milk, each spectrum also provides a reservoir of unharnessed information about the sample. The accumulation and subsequent interpretation of these data present some challenges due to their high-dimensionality and the relationships amongst the spectral variables. In this work, directly motivated by a dairy application, we propose a modification of the standard factor analysis to induce a parsimonious summary of spectroscopic data. Our proposal maps the observations into a low-dimensional latent space while simultaneously clustering the observed variables. The method indicates possible redundancies in the data, and it helps disentangle the complex relationships among the wavelengths. A flexible Bayesian estimation procedure is proposed for model fitting, providing reasonable values for the number of latent factors and clusters. The method is applied on milk mid-infrared (MIR) spectroscopy data from dairy cows on distinctly different pasture and nonpasture based diets, providing accurate modelling of the correlation, clustering of variables, and information on differences among milk samples from cows on different diets.