For psychiatric diseases, established mechanistic models are lacking and alternative empirical mathematical structures are usually explored by a trial-and-error procedure. To address this problem, one of the most promising approaches is an automated model-free technique that extracts the model structure directly from the statistical properties of the data. In this paper, a linear-in-parameter modelling approach is developed based on principal component analysis (PCA). The model complexity, i.e. the number of components entering the PCA-based model, is selected by either cross-validation or Mallows' Cp criterion. This new approach has been validated on both simulated and clinical data taken from a Phase II depression trial. Simulated datasets are generated through three parametric models: Weibull, Inverse Bateman and Weibull-and-Linear. In particular, concerning simulated datasets, it is found that the PCA approach compares very favourably with some of the popular parametric models used for analyzing data collected during psychiatric trials. Furthermore, the proposed method performs well on the experimental data. This approach can be useful whenever a mechanistic modelling procedure cannot be pursued. Moreover, it could support subsequent semi-mechanistic model building.