We explore structural issues with parameter estimation fornon-linear cognitive models: Some parameter values are eas-ier to recover than others, and the recoverability of differentparameters interacts in systematic ways. We propose methodsfor researchers to anticipate and visualize and these issues, andthe systematic ways they differ across experimental designs.Our approach consists of assessing how changes in parame-ter values translate into changes in behavioral predictions, anddevelop measurements of the relative responsiveness of predic-tions to parameter values. We demonstrate application of ourapproach to cumulative prospect theory (CPT), a widely-usedmodel of risky decision-making.