Fitting a polytomous item response model to Likert-type data

This study examined the application of the MML-EM algorithm to the parameter estimation problems of the normal ogive and logistic polytomous response models for Likert-type items. A rating-scale model was developed based on Samejima’s (1969) graded response model. The graded response model includes a separate slope parameter for each item and an item response parameter. In the rating-scale model, the item response parameter is resolved into two parameters: the item location parameter, and the category threshold parameter characterizing the boundary between response categories. For a Likert-type questionnaire, where a single scale is employed to elicit different responses to the items, this item response model is expected to be more useful for analysis because the item parameters can be estimated separately from the threshold parameters associated with the points on a single Likert scale. The advantages of this type of model are shown by analyzing simulated data and data from the General Social Surveys. Index terms: EM algorithm, General Social Surveys, graded response model, item response model, Likert scale, marginal maximum likelihood, polytomous item response model, rating-scale model