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The under-determined estimation problem

The matrix estimation problem is not always an easy one to solve. Most users will find that the Analyst Drive software works very well for their application, but the nature of the problem itself provides the estimation procedure with very under-determined systems that can make it difficult or simply impossible to improve upon the OD matrix in cases where there simply is not enough data for the number of matrix entries the user wishes to estimate. To produce good results, the modeler should provide an adequate amount of input data for the problem they wish to solve. In general, the estimation will perform better when the ratio of available data counts to the number of OD entries to be estimated is closer to 1. In fact, in the case that a one-to-one ratio of counts to design variables is available then one could actually solve the equations exactly. This is of course a dream scenario and not something encountered in practice, but nonetheless, the more available data points the better the estimation results. The remainder of this section discusses some more advanced issues dealing with Analyst Drive runs, and is intended to help the user better use and better understand the program results and performance.