Modern statistical problems regularly involve data collected with more structure than simple scalars, for example functional or image data. Accompanying these more exotic data types has been the generalisation of statistical methods to analyse data which take values in almost arbitrary Hilbert spaces. Yet to date, nearly all regression approaches treat a single, often specific, data type within a single Hilbert space. This work considers a linear framework for statistical analysis of data objects naturally represented in a variety of Hilbert spaces, using latent space projections. As part of this framework, we generalise the method of Partial Least Squares and demonstrate its use on data related to estimating early Alzheimer’s disease.