How challenging is modeling of a data set?

We introduce a novel methodology for determining the difficulty of modeling a given data set. The method utilizes formulation of modeling as an optimization problem instance that consists of an objective function and a set of constraints. The properties of the data set that could affect the quality of optimization are categorized. In large optimization problems with multiple properties that contribute to the solution quality, it is practically impossible to analytically study the effect of each property. A number of metrics for evaluating the effectiveness of the optimization on each data set are proposed. Using the well known Plackett and Burmann fast simulation methodology, for each metric, the impact of the categorized properties of the data are determined for the specified optimization method. A new approach for combining the impacts resulting from different properties on various metrics is described. The method is illustrated on distance measurement data used for estimating the locations of wireless nodes in ad-hoc networks.