We explore structural issues with parameter estimation for non-linear cognitive models: Some parameter values are easier to recover than others, and the recoverability of different parameters interacts in systematic ways. We propose methods for researchers to anticipate and visualize and these issues, and the systematic ways they differ across experimental designs. Our approach consists of assessing how changes in parameter values translate into changes in behavioral predictions, and develop measurements of the relative responsiveness of predictions to parameter values. We demonstrate application of our approach to cumulative prospect theory (CPT), a widely-used model of risky decision-making.