Dimensionality reduction techniques have found great success in a wide range of fields requiring analysis of high-dimensional datasets. Time-lagged independent components analysis (TICA), which finds independent components (TICs) with maximal autocorrelation, is often applied to atomistic biomolecular simulations, where the full molecular configuration can be projected onto only a few TICs describing the slowest modes of motion. Recently, Sultan and Pande have proposed the use of TICs as collective variables for enhanced sampling. However, it is unclear what the best strategy for estimating the TICs of a system is a priori. In order to evaluate the utility of TICs calculated on one system to describe the slow dynamics of similar systems, we develop a methodology for measuring the transferability of TICs and apply it to a wide range of systems. We find that transferred TICs can approximate the slowest dynamics of some systems surprisingly well, while failing to transfer between other sets of systems, highlighting the inherent difficulties of predicting TIC transferability. Additionally, we use two dimensional Brownian dynamics simulations on similar potential surfaces to gain insight into the relationship between TIC transferability and potential surface changes.