Abstract: Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA+ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate this model, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation are achieved simultaneously. Our method orders components by their marginal likelihood in a manner that parallels the ordering of components by variance used in principal component analysis (PCA). We present a semi-parametric LCA in which the log densities are estimated using cubic B-splines. In simulations, latent components are recovered that are discarded by PCA+ICA methods. We apply our method to a multivariate dataset on leaf attributes and demonstrate that LCA is a useful data visualization and dimension reduction tool that reveals features not apparent from PCA or PCA+ICA. We also apply our method to an fMRI experiment from the Human Connectome Project and identify artifacts missed by PCA+ICA.