Mathematical modeling of behavior during a psychophysical task, referred to as "computational psychiatry," could greatly improve our understanding of mental disorders. One barrier to the broader adoption of computational methods, is that they often require advanced statistical modeling and mathematical skills. Biological and behavioral signals often show skewed or non-Gaussian distributions, and very few toolboxes and analytical platforms are capable of processing such signal categories. We developed the Computational Psychiatry Adaptive State-Space (COMPASS) toolbox, an open-source MATLAB-based software package. This toolbox is easy to use and capable of integrating signals with a variety of distributions. COMPASS has the tools to process signals with continuous-valued and binary measurements, or signals with incomplete-missing or censored-measurements, which makes it well-suited for processing those signals captured during a psychophysical task. After specifying a few parameters in a small set of user-friendly functions, COMPASS allows users to efficiently apply a wide range of computational behavioral models. The model output can be analyzed as an experimental outcome or used as a regressor for neural data and can also be tested using the goodness-of-fit measurement. Here, we demonstrate that COMPASS can replicate two computational behavioral analyses from different groups. COMPASS replicates and can slightly improve on the original modeling results. We also demonstrate the use of COMPASS application in a censored-data problem and compare its performance result with naïve estimation methods. This flexible, general-purpose toolkit should accelerate the use of computational modeling in psychiatric neuroscience.