The Graded Item Response
Up to this point, the presentation has been limited to free response items that have been dichotomously scored. This scoring procedure was based on the assumption that a continuous hypothetical item variable for item i, ri , underlies the examinee's response, but the only manifest data available is the correctness of the response. Such binary items are the mainstay of educational and psychological testing; however, other item scoring procedures, such as the graded and nominal response cases, can also be employed. Under the graded scoring procedure, the hypothetical item variable scale is divided into ordered categories. Thus, the lowest category would contribute the least to a person's test score while the highest category would contribute the most. The Likert-type item traditionally used in questionnaires, attitude inventories, and surveys is a classic example of an item whose responses are scored in a graded fashion. In such items, a scale is used, and the labeling imparts the order, such as strongly disagree, disagree, indifferent, agree, and strongly agree. A weight of 1 would be assigned to strongly disagree, 2 to disagree, and so on until strongly agree is assigned a weight of 5. When nominal scoring is used, it is assumed that item responses can be categorized, but the categories are not ordered. From an intuitive point of view, there is a progression from dichotomous to graded to nominal scoring of item responses. The present chapter will deal only with the graded response case, while the nominal response will be presented in the next chapter.