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Assessments with ratings in ordered categories have become ubiquitous in health, biological and social sciences. Ratings are used when a measuring instrument of the kind found in the natural sciences is not available to assess some property in terms of degree - for example, greater or smaller, better or worse, or stronger or weaker. The handling of ratings has ranged from the very elementary to the highly sophisticated. In an elementary form, and assumed in classical test theory, the ratings are scored with successive integers and treated as measurements; in a sophisticated form, and used in modern test theory, the ratings are characterized by probabilistic response models with parameters for persons and the rating categories. Within modern test theory, two paradigms, similar in many details but incompatible on crucial points, have emerged. For the purposes of this article, these are termed the statistical modeling and experimental measurement paradigms. Rather than reviewing a compendium of available methods and models for analyzing ratings in detail, the article focuses on the incompatible differences between these two paradigms, with implications for choice of model and inferences. It shows that the differences have implications for different roles for substantive researchers and psychometricians in designing instruments with rating scales. To illustrate these differences, an example is provided.
A latent trait measurement model in which ordered response categories are both parameterized and scored with successive integers is investigated and applied to a summated rating or Likert ques tionnaire. In addition to each category, each item of the questionnaire and each subject are para meterized in the model; and maximum likelihood estimates for these parameters are derived. Among the features of the model which make it attractive for applications to Likert questionnaires is that the total score is a sufficient statistic for a subject's at titude measure. Thus, the model provides a formal ization of a familiar and practical procedure for measuring attitudes.
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