Recent years have seen a growing interest in methods for predicting a variable of interest, such as a subject’s age, from individual brain scans. Although the field has focused strongly on nonlinear discriminative methods using deep learning, here we explore whether linear generative techniques can be used as practical alternatives that are easier to tune, train and interpret. The models we propose consist of (1) a causal forward model expressing the effect of variables of interest on brain morphology, and (2) a latent variable noise model, based on factor analysis, that is quick to learn and invert. In experiments estimating individuals’ age and gender from the UK Biobank dataset, we demonstrate competitive prediction performance even when the number of training subjects is in the thousands – the typical scenario in many potential applications. The method is easy to use as it has only a single hyperparameter, and directly estimates interpretable spatial maps of the underlying structural changes that are driving the predictions.