This study examines the application of the marginal maximum likelihood (MML) EM algorithm to the parameter estimation problem of the three-parameter normal ogive and logistic polychotomous item response models. A three-parameter normal ogive model, the Graded Response model, has been developed on the basis of Samejima's two-parameter graded response model. A three-parameter logistic model, the Rating Scale model, has been developed based on Andrich's Rasch polychotomous response model. In the three-parameter models, an item response parameter is resolved into two parameters: item location and category (step). In the case of the Likert-type questionnaire, where only a single scale is employed to evoke different responses for test items, the three-parameter model is expected to be more useful in terms of prediction and analysis because the estimates of the slope and location parameters associated with the points on a single Likert scale can be separately estimated. The advantages of this type of model are demonstrated by analyzing actual data sets. An extension of measurement models of analytic models is also discussed. In a specific analytic model, based on the Graded Response Model, the structural item response model, the design matrix is incorporated to represent a structure among subject groups. (Author)