  In recent years animal diet has been receiving increased attention, in
particular examining the impact of pasture-based feeding strategies on the
quality of milk and dairy products, in line with the increased prevalence of
grass-fed dairy products appearing on market shelves. To date, there are
limited testing methods available for the verification of grass-fed dairy
therefore these products are susceptible to food fraud and adulteration. Hence
statistical tools studying potential differences among milk samples coming from
animals on different feeding systems are required, thus providing increased
security around the authenticity of the products. Infrared spectroscopy
techniques are widely used to collect data on milk samples and to predict milk
related traits. While these data are routinely used to predict the composition
of the macro components of milk, each spectrum provides a reservoir of
unharnessed information about the sample. The interpretation of these data
presents a number of challenges due to their high-dimensionality and the
relationships amongst the spectral variables. In this work we propose a
modification of the standard factor analysis to induce a parsimonious summary
of spectroscopic data. The procedure maps the observations into a
low-dimensional latent space while simultaneously clustering 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 spectroscopy data from dairy cows on different
pasture and non-pasture based diets, providing accurate modelling of the data
correlation, the clustering of variables and information on differences between
milk samples from cows on different diets.
