In this article, a latent trait model is proposed for the response times in psychological tests. The latent trait model is based on the linear transformation model and subsumes popular models from survival analysis, like the proportional hazards model and the proportional odds model. Core of the model is the assumption that an unspecified monotone transformation of the response times can be related to latent characteristics of the test taker. The model can be interpreted in terms of an information accumulation process, according to which test takers acquire information until they are able to respond. The rate of information accumulation can be related to the transformation function of the response times. In order to avoid strong distributional assumptions, the rate of information acquisition is approximated in a piecewise manner by a positive spline. The model can be calibrated with marginal maximum likelihood estimation. This allows a standard test of model fit as will be shown. The proposed approach to model estimation and model evaluation is investigated in a simulation study. Finally, the utility of the model is demonstrated in three real data sets.