Cognitive process models are fit to observed data to infer how experimental manipulations modify the assumed underlying cognitive process. They are alternatives to descriptive models, which only capture differences on the observed data level, and do not make assumptions about the underlying cognitive process. Process models may require more observations than descriptive models however , and as a consequence, usually fewer conditions can be simultaneously modeled with them. Unfortunately, it is known that the predictive validity of a model may be compromised when fewer experimental conditions are jointly accounted for (e.g., overestimation of predictor effects, or their incorrect assignment). We develop a hierarchical and covaried multiple regression approach to address this problem. Specifically, we show how to map the recurrences of all conditions, participants, items, and/or traits across experimental design cells to the process model parameters. This systematic pooling of information can facilitate parameter estimation. The proposed approach is particularly relevant for multi-factor experimental designs, and for mixture models that parameterize per cell to assess predictor effects. This hierarchical framework provides the capacity to model more conditions jointly to improve parameter recovery atlow observation numbers (e.g., using only 1/6 of trials,recovering as well as standard hierarchical Bayesian meth-ods), and to directly model predictor and covariate effects onthe process parameters, without the need for post hoc anal-yses (e.g., ANOVA). An example application to real data isalso provided.