Many combinations of a method and an approach for estimating the operating characteristics of the graded item responses, without assuming any mathematical forms, have been produced. In these methods, a set of items whose characteristics are known, or Old Test, is used, which has a large, constant amount of test information throughout the interval of the latent trait of interest. The rationale is presented to generalize these methods so that they are made applicable when the test information of the Old Test is not constant. Both the transformation-free character of the maximum likelihood estimator and the method of moments for fitting a polynomial as the least squares solution play important roles in this rationale. Comparison of results using different types of test information functions are presented. The procedures presented in this paper will be applied in a simulation study, and published as separate papers, in order to investigate how the theory works in practice. (Author/RL)