In recent years there has been growing interest in multivariate analyses of neuroimaging data, which can be used to detect distributed patterns of activity that encode an experimental factor of interest. In this setting, it has become common practice to study the correlations between patterns to make inferences about the way a brain region represents stimuli or tasks (known as representational similarity analysis). Although it would be of great interest to compare these correlations from different regions, direct comparisons are currently not possible. This is because sample correlations are strongly influenced by voxel-selection, fMRI noise, and nonspecific activation patterns, all of which can differ widely between regions. Here, we present a multivariate modeling framework in which the measured patterns are decomposed into their constituent parts. The model is based on a standard linear mixed model, in which pattern components are considered to be randomly distributed over voxels. The model allows one to estimate the true correlations of the underlying neuronal pattern components, thereby enabling comparisons between different regions or individuals. The pattern estimates also allow us to make inferences about the spatial structure of different response components. Thus, the new model provides a theoretical and analytical framework to study the structure of distributed neural representations.